DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

Two statistical mechanics aspects of complex networks

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Biely, Christoly

2006-12-01

By adopting an ensemble interpretation of non-growing rewiring networks, network theory can be reduced to a counting problem of possible network states and an identification of their associated probabilities. We present two scenarios of how different rewirement schemes can be used to control the state probabilities of the system. In particular, we review how by generalizing the linking rules of random graphs, in combination with superstatistics and quantum mechanical concepts, one can establish an exact relation between the degree distribution of any given network and the nodes’ linking probability distributions. In a second approach, we control state probabilities by a network Hamiltonian, whose characteristics are motivated by biological and socio-economical statistical systems. We demonstrate that a thermodynamics of networks becomes a fully consistent concept, allowing to study e.g. ‘phase transitions’ and computing entropies through thermodynamic relations.

Neural Correlates of the Divergence of Instrumental Probability Distributions

PubMed Central

Wang, Shuo; Zhang, June; O'Doherty, John P.

2013-01-01

Flexible action selection requires knowledge about how alternative actions impact the environment: a “cognitive map” of instrumental contingencies. Reinforcement learning theories formalize this map as a set of stochastic relationships between actions and states, such that for any given action considered in a current state, a probability distribution is specified over possible outcome states. Here, we show that activity in the human inferior parietal lobule correlates with the divergence of such outcome distributions–a measure that reflects whether discrimination between alternative actions increases the controllability of the future–and, further, that this effect is dissociable from those of other information theoretic and motivational variables, such as outcome entropy, action values, and outcome utilities. Our results suggest that, although ultimately combined with reward estimates to generate action values, outcome probability distributions associated with alternative actions may be contrasted independently of valence computations, to narrow the scope of the action selection problem. PMID:23884955

A Gaussian measure of quantum phase noise

NASA Technical Reports Server (NTRS)

Schleich, Wolfgang P.; Dowling, Jonathan P.

1992-01-01

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study.

PubMed

Miśkiewicz, Janusz; Trela, Zenon; Przestalski, Stanisław; Karcz, Waldemar

2010-09-01

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met(3)PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met(3)PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Steady-state distributions of probability fluxes on complex networks

NASA Astrophysics Data System (ADS)

Chełminiak, Przemysław; Kurzyński, Michał

2017-02-01

We consider a simple model of the Markovian stochastic dynamics on complex networks to examine the statistical properties of the probability fluxes. The additional transition, called hereafter a gate, powered by the external constant force breaks a detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge to the Gaussian distribution. By virtue of the stationary fluctuation theorem, its standard deviation depends directly on the square root of the mean flux. In turn, the nonlinear relation between the mean flux and the external force, which provides the key result of the present study, allows us to calculate the two parameters that entirely characterize the Gaussian distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of computer simulations are widely discussed in terms of the rigorous theoretical predictions.

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multiple Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multipath Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

Statistics of work performed on a forced quantum oscillator.

PubMed

Talkner, Peter; Burada, P Sekhar; Hänggi, Peter

2008-07-01

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the corresponding probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical, and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may greatly differ. This result in particular also holds true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed.

Comparison of three-parameter probability distributions for representing annual extreme and partial duration precipitation series

NASA Astrophysics Data System (ADS)

Wilks, Daniel S.

1993-10-01

Performance of 8 three-parameter probability distributions for representing annual extreme and partial duration precipitation data at stations in the northeastern and southeastern United States is investigated. Particular attention is paid to fidelity on the right tail, through use of a bootstrap procedure simulating extrapolation on the right tail beyond the data. It is found that the beta-κ distribution best describes the extreme right tail of annual extreme series, and the beta-P distribution is best for the partial duration data. The conventionally employed two-parameter Gumbel distribution is found to substantially underestimate probabilities associated with the larger precipitation amounts for both annual extreme and partial duration data. Fitting the distributions using left-censored data did not result in improved fits to the right tail.

Quantum probability assignment limited by relativistic causality.

PubMed

Han, Yeong Deok; Choi, Taeseung

2016-03-14

Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.

Misinterpretation of statistical distance in security of quantum key distribution shown by simulation

NASA Astrophysics Data System (ADS)

Iwakoshi, Takehisa; Hirota, Osamu

2014-10-01

This study will test an interpretation in quantum key distribution (QKD) that trace distance between the distributed quantum state and the ideal mixed state is a maximum failure probability of the protocol. Around 2004, this interpretation was proposed and standardized to satisfy both of the key uniformity in the context of universal composability and operational meaning of the failure probability of the key extraction. However, this proposal has not been verified concretely yet for many years while H. P. Yuen and O. Hirota have thrown doubt on this interpretation since 2009. To ascertain this interpretation, a physical random number generator was employed to evaluate key uniformity in QKD. In this way, we calculated statistical distance which correspond to trace distance in quantum theory after a quantum measurement is done, then we compared it with the failure probability whether universal composability was obtained. As a result, the degree of statistical distance of the probability distribution of the physical random numbers and the ideal uniformity was very large. It is also explained why trace distance is not suitable to guarantee the security in QKD from the view point of quantum binary decision theory.

A Seakeeping Performance and Affordability Tradeoff Study for the Coast Guard Offshore Patrol Cutter

DTIC Science & Technology

2016-06-01

Index Polar Plot for Sea State 4, All Headings Are Relative to the Wave Motion and Velocity is Given in Meters per Second...40 Figure 15. Probability and Cumulative Density Functions of Annual Sea State Occurrences in the Open Ocean, North Pacific...criteria at a given sea state. Probability distribution functions are available that describe the likelihood that an operational area will experience

Tomographic measurement of joint photon statistics of the twin-beam quantum state

PubMed

Vasilyev; Choi; Kumar; D'Ariano

2000-03-13

We report the first measurement of the joint photon-number probability distribution for a two-mode quantum state created by a nondegenerate optical parametric amplifier. The measured distributions exhibit up to 1.9 dB of quantum correlation between the signal and idler photon numbers, whereas the marginal distributions are thermal as expected for parametric fluorescence.

A dynamic programming approach to estimate the capacity value of energy storage

DOE PAGES

Sioshansi, Ramteen; Madaeni, Seyed Hossein; Denholm, Paul

2013-09-17

Here, we present a method to estimate the capacity value of storage. Our method uses a dynamic program to model the effect of power system outages on the operation and state of charge of storage in subsequent periods. We combine the optimized dispatch from the dynamic program with estimated system loss of load probabilities to compute a probability distribution for the state of charge of storage in each period. This probability distribution can be used as a forced outage rate for storage in standard reliability-based capacity value estimation methods. Our proposed method has the advantage over existing approximations that itmore » explicitly captures the effect of system shortage events on the state of charge of storage in subsequent periods. We also use a numerical case study, based on five utility systems in the U.S., to demonstrate our technique and compare it to existing approximation methods.« less

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

NASA Technical Reports Server (NTRS)

Nemeth, Noel

2013-01-01

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Measurement of Plutonium-240 Angular Momentum Dependent Fission Probabilities Using the Alpha-Alpha' Reaction

NASA Astrophysics Data System (ADS)

Koglin, Johnathon

Accurate nuclear reaction data from a few keV to tens of MeV and across the table of nuclides is essential to a number of applications of nuclear physics, including national security, nuclear forensics, nuclear astrophysics, and nuclear energy. Precise determination of (n, f) and neutron capture cross sections for reactions in high- ux environments are particularly important for a proper understanding of nuclear reactor performance and stellar nucleosynthesis. In these extreme environments reactions on short-lived and otherwise difficult-to-produce isotopes play a significant role in system evolution and provide insights into the types of nuclear processes taking place; a detailed understanding of these processes is necessary to properly determine cross sections far from stability. Indirect methods are often attempted to measure cross sections on isotopes that are difficult to separate in a laboratory setting. Using the surrogate approach, the same compound nucleus from the reaction of interest is created through a "surrogate" reaction on a different isotope and the resulting decay is measured. This result is combined with appropriate reaction theory for compound nucleus population, from which the desired cross sections can be inferred. This method has shown promise, but the theoretical framework often lacks necessary experimental data to constrain models. In this work, dual arrays of silicon telescope particle identification detectors and photovoltaic (solar) cell fission fragment detectors have been used to measure the fission probability of the 240Pu(alpha, alpha'f) reaction - a surrogate for the 239Pu(n, f) - and fission of 35.9(2)MeV at eleven scattering angles from 40° to 140° in 10° intervals and at nuclear excitation energies up to 16MeV. Within experimental uncertainty, the maximum fission probability was observed at the neutron separation energy for each alpha scattering angle. Fission probabilities were separated into five 500 keV bins from 5:5MeV to 8:0MeV and one bin from 4:5MeV to 5:5MeV. Across energy bins the fission probability increases approximately linearly with increasing alpha' scattering angle. At 90° the fission probability increases from 0:069(6) in the lowest energy bin to 0:59(2) in the highest. Likewise, within a single energy bin the fission probability increases with alpha' scattering angle. Within the 6:5MeV and 7:0MeV energy bin, the fission probability increased from 0:41(1) at 60° to 0:81(10) at 140°. Fission fragment angular distributions were also measured integrated over each energy bin. These distributions were fit to theoretical distributions based on combinations of transitional nuclear vibrational and rotational excitations at the saddle point. Contributions from specific K vibrational states were extracted and combined with fission probability measurements to determine the relative fission probability of each state as a function of nuclear excitation energy. Within a given excitation energy bin, it is found that contributions from K states greater than the minimum K = 0 state tend to increase with the increasing alpha' scattering angle. This is attributed to an increase in the transferred angular momentum associated with larger scattering angles. The 90° alpha' scattering angle produced the highest quality results. The relative contributions of K states do not show a discernible trend across the energy spectrum. The energy-binned results confirm existing measurements that place a K = 2 state in the first energy bin with the opening of K = 1 and K = 4 states at energies above 5:5MeV. This experiment represents the first of its kind in which fission probabilities and angular distributions are simultaneously measured at a large number of scattering angles. The acquired fission probability, angular distribution, and K state contribution provide a diverse dataset against which microscopic fission models can be constrained and further the understanding of the properties of the 240Pu fission.

Average fidelity between random quantum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zyczkowski, Karol; Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Aleja Lotnikow 32/44, 02-668 Warsaw; Perimeter Institute, Waterloo, Ontario, N2L 2Y5

2005-03-01

We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: the Hilbert-Schmidt measure, the Bures (statistical) measure, the measure induced by the partial trace, and the natural measure on the space of pure states. In certain cases explicit probability distributions for the fidelity are derived. The results obtained may be used to gauge the quality of quantum-information-processing schemes.

Wigner functions for nonclassical states of a collection of two-level atoms

NASA Technical Reports Server (NTRS)

Agarwal, G. S.; Dowling, Jonathan P.; Schleich, Wolfgang P.

1993-01-01

The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.

Open quantum random walk in terms of quantum Bernoulli noise

NASA Astrophysics Data System (ADS)

Wang, Caishi; Wang, Ce; Ren, Suling; Tang, Yuling

2018-03-01

In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897-1908, 2016) as a special case.

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

PubMed

Jacobsen, J L; Saleur, H

2008-02-29

We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.

Exploring image data assimilation in the prospect of high-resolution satellite oceanic observations

NASA Astrophysics Data System (ADS)

Durán Moro, Marina; Brankart, Jean-Michel; Brasseur, Pierre; Verron, Jacques

2017-07-01

Satellite sensors increasingly provide high-resolution (HR) observations of the ocean. They supply observations of sea surface height (SSH) and of tracers of the dynamics such as sea surface salinity (SSS) and sea surface temperature (SST). In particular, the Surface Water Ocean Topography (SWOT) mission will provide measurements of the surface ocean topography at very high-resolution (HR) delivering unprecedented information on the meso-scale and submeso-scale dynamics. This study investigates the feasibility to use these measurements to reconstruct meso-scale features simulated by numerical models, in particular on the vertical dimension. A methodology to reconstruct three-dimensional (3D) multivariate meso-scale scenes is developed by using a HR numerical model of the Solomon Sea region. An inverse problem is defined in the framework of a twin experiment where synthetic observations are used. A true state is chosen among the 3D multivariate states which is considered as a reference state. In order to correct a first guess of this true state, a two-step analysis is carried out. A probability distribution of the first guess is defined and updated at each step of the analysis: (i) the first step applies the analysis scheme of a reduced-order Kalman filter to update the first guess probability distribution using SSH observation; (ii) the second step minimizes a cost function using observations of HR image structure and a new probability distribution is estimated. The analysis is extended to the vertical dimension using 3D multivariate empirical orthogonal functions (EOFs) and the probabilistic approach allows the update of the probability distribution through the two-step analysis. Experiments show that the proposed technique succeeds in correcting a multivariate state using meso-scale and submeso-scale information contained in HR SSH and image structure observations. It also demonstrates how the surface information can be used to reconstruct the ocean state below the surface.

Energy Distributions in Small Populations: Pascal versus Boltzmann

ERIC Educational Resources Information Center

Kugel, Roger W.; Weiner, Paul A.

2010-01-01

The theoretical distributions of a limited amount of energy among small numbers of particles with discrete, evenly-spaced quantum levels are examined systematically. The average populations of energy states reveal the pattern of Pascal's triangle. An exact formula for the probability that a particle will be in any given energy state is derived.…

The concept of entropy in landscape evolution

USGS Publications Warehouse

Leopold, Luna Bergere; Langbein, Walter Basil

1962-01-01

The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.

Metabolic networks evolve towards states of maximum entropy production.

PubMed

Unrean, Pornkamol; Srienc, Friedrich

2011-11-01

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles. Copyright © 2011 Elsevier Inc. All rights reserved.

A discussion on the origin of quantum probabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holik, Federico, E-mail: olentiev2@gmail.com; Departamento de Matemática - Ciclo Básico Común, Universidad de Buenos Aires - Pabellón III, Ciudad Universitaria, Buenos Aires; Sáenz, Manuel

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivationmore » of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases.« less

Structural changes and fluctuations of proteins. I. A statistical thermodynamic model.

PubMed

Ikegami, A

1977-01-01

A general theory of the structural changes and fluctuations of proteins has been proposed based on statistical thermodynamic considerations at the chain level. The "structure" of protein was assumed to be characterized by the state of secondary bonds between unique pairs of specific sites on peptide chains. Every secondary bond changes between the bonded and unbonded states by thermal agitation and the "structure" is continuously fluctuating. The free energy of the "structural state" that is defined by the fraction of secondary bonds in the bonded state has been expressed by the bond energy, the cooperative interaction between bonds, the mixing entropy of bonds, and the entropy of polypeptide chains. The most probable "structural state" can be simply determined by graphical analysis and the effect of temperature or solvent composition on it is discussed. The temperature dependence of the free energy, the probability distribution of structural states and the specific heat have been calculted for two examples of structural change. The theory predicts two different types of structural changes from the ordered to disorderd state, a "structured transition" and a "gradual structural change" with rising temperature. In the "structural transition", the probability distribution has two maxima in the temperature range of transition. In the "gradual structural change", the probabilty distribution has only one maximum during the change. A considerable fraction of secondary bonds is in the unbounded state and is always fluctuating even in the ordered state at room temperature. Such structural flucutations in a single protein molecule have been discussed quantitatively. The theory is extended to include small molecules which bind to the protein molecule and affect the structural state. The changes of structural state caused by specific and non-specific binding and allosteric effects are explained in a unified manner.

Measurement of 240Pu Angular Momentum Dependent Fission Probabilities Using the (α ,α') Reaction

NASA Astrophysics Data System (ADS)

Koglin, Johnathon; Burke, Jason; Fisher, Scott; Jovanovic, Igor

2017-09-01

The surrogate reaction method often lacks the theoretical framework and necessary experimental data to constrain models especially when rectifying differences between angular momentum state differences between the desired and surrogate reaction. In this work, dual arrays of silicon telescope particle identification detectors and photovoltaic (solar) cell fission fragment detectors have been used to measure the fission probability of the 240Pu(α ,α' f) reaction - a surrogate for the 239Pu(n , f) - and fission fragment angular distributions. Fission probability measurements were performed at a beam energy of 35.9(2) MeV at eleven scattering angles from 40° to 140°e in 10° intervals and at nuclear excitation energies up to 16 MeV. Fission fragment angular distributions were measured in six bins from 4.5 MeV to 8.0 MeV and fit to expected distributions dependent on the vibrational and rotational excitations at the saddle point. In this way, the contributions to the total fission probability from specific states of K angular momentum projection on the symmetry axis are extracted. A sizable data collection is presented to be considered when constraining microscopic cross section calculations.

Decision theory for computing variable and value ordering decisions for scheduling problems

NASA Technical Reports Server (NTRS)

Linden, Theodore A.

1993-01-01

Heuristics that guide search are critical when solving large planning and scheduling problems, but most variable and value ordering heuristics are sensitive to only one feature of the search state. One wants to combine evidence from all features of the search state into a subjective probability that a value choice is best, but there has been no solid semantics for merging evidence when it is conceived in these terms. Instead, variable and value ordering decisions should be viewed as problems in decision theory. This led to two key insights: (1) The fundamental concept that allows heuristic evidence to be merged is the net incremental utility that will be achieved by assigning a value to a variable. Probability distributions about net incremental utility can merge evidence from the utility function, binary constraints, resource constraints, and other problem features. The subjective probability that a value is the best choice is then derived from probability distributions about net incremental utility. (2) The methods used for rumor control in Bayesian Networks are the primary way to prevent cycling in the computation of probable net incremental utility. These insights lead to semantically justifiable ways to compute heuristic variable and value ordering decisions that merge evidence from all available features of the search state.

Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Schwartz, Robert N.; Wang, Kang L.

2016-03-01

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.

A Brownian model for recurrent earthquakes

USGS Publications Warehouse

Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.

2002-01-01

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may be much stronger than would be predicted by the "clock change" method and characteristically decay inversely with elapsed time after the perturbation.

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nair, Ranjith

2011-09-15

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas formore » the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N{sub s}, the fidelity is minimized by any multimode Fock state with N{sub s} total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances. The experimental outlook for realizing nonclassical gains from number state transmitters with current technology at moderate to high values of the reflectances is argued to be good.« less

Dynamics of coherent states in regular and chaotic regimes of the non-integrable Dicke model

NASA Astrophysics Data System (ADS)

Lerma-Hernández, S.; Chávez-Carlos, J.; Bastarrachea-Magnani, M. A.; López-del-Carpio, B.; Hirsch, J. G.

2018-04-01

The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.

A Financial Market Model Incorporating Herd Behaviour.

PubMed

Wray, Christopher M; Bishop, Steven R

2016-01-01

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents' accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents' accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.

A Vehicle for Bivariate Data Analysis

ERIC Educational Resources Information Center

Roscoe, Matt B.

2016-01-01

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

Oil spill contamination probability in the southeastern Levantine basin.

PubMed

Goldman, Ron; Biton, Eli; Brokovich, Eran; Kark, Salit; Levin, Noam

2015-02-15

Recent gas discoveries in the eastern Mediterranean Sea led to multiple operations with substantial economic interest, and with them there is a risk of oil spills and their potential environmental impacts. To examine the potential spatial distribution of this threat, we created seasonal maps of the probability of oil spill pollution reaching an area in the Israeli coastal and exclusive economic zones, given knowledge of its initial sources. We performed simulations of virtual oil spills using realistic atmospheric and oceanic conditions. The resulting maps show dominance of the alongshore northerly current, which causes the high probability areas to be stretched parallel to the coast, increasing contamination probability downstream of source points. The seasonal westerly wind forcing determines how wide the high probability areas are, and may also restrict these to a small coastal region near source points. Seasonal variability in probability distribution, oil state, and pollution time is also discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation

NASA Astrophysics Data System (ADS)

Jiang, Cong; Yu, Zong-Wen; Wang, Xiang-Bin

2017-03-01

We show how to calculate the secure final key rate in the four-intensity decoy-state measurement-device-independent quantum key distribution protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without assuming any specific error patterns of the source.

A methodology for stochastic analysis of share prices as Markov chains with finite states.

PubMed

Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey

2014-01-01

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

NASA Astrophysics Data System (ADS)

Salimi, S.; Jafarizadeh, M. A.

2009-06-01

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete Kn, charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied.

Globally coupled stochastic two-state oscillators: fluctuations due to finite numbers.

PubMed

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N → ∞ and t → ∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

NASA Astrophysics Data System (ADS)

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N →∞ and t →∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Load sharing in distributed real-time systems with state-change broadcasts

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Chang, Yi-Chieh

1989-01-01

A decentralized dynamic load-sharing (LS) method based on state-change broadcasts is proposed for a distributed real-time system. Whenever the state of a node changes from underloaded to fully loaded and vice versa, the node broadcasts this change to a set of nodes, called a buddy set, in the system. The performance of the method is evaluated with both analytic modeling and simulation. It is modeled first by an embedded Markov chain for which numerical solutions are derived. The model solutions are then used to calculate the distribution of queue lengths at the nodes and the probability of meeting task deadlines. The analytical results show that buddy sets of 10 nodes outperform those of less than 10 nodes, and the incremental benefit gained from increasing the buddy set size beyond 15 nodes is insignificant. These and other analytical results are verified by simulation. The proposed LS method is shown to meet task deadlines with a very high probability.

Activated recombinative desorption: A potential component in mechanisms of spacecraft glow

NASA Technical Reports Server (NTRS)

Cross, J. B.

1985-01-01

The concept of activated recombination of atomic species on surfaces can explain the production of vibrationally and translationally excited desorbed molecular species. Equilibrium statistical mechanics predicts that the molecular quantum state distributions of desorbing molecules is a function of surface temperature only when the adsorption probability is unity and independent of initial collision conditions. In most cases, the adsorption probability is dependent upon initial conditions such as collision energy or internal quantum state distribution of impinging molecules. From detailed balance, such dynamical behavior is reflected in the internal quantum state distribution of the desorbing molecule. This concept, activated recombinative desorption, may offer a common thread in proposed mechanisms of spacecraft glow. Using molecular beam techniques and equipment available at Los Alamos, which includes a high translational energy 0-atom beam source, mass spectrometric detection of desorbed species, chemiluminescence/laser induced fluorescence detection of electronic and vibrationally excited reaction products, and Auger detection of surface adsorbed reaction products, a fundamental study of the gas surface chemistry underlying the glow process is proposed.

Sexual differentiation in the distribution potential of northern jaguars (Panthera onca)

Treesearch

Erin E. Boydston; Carlos A. Lopez Gonzalez

2005-01-01

We estimated the potential geographic distribution of jaguars in the southwestern United States and northwestern Mexico by modeling the jaguar ecological niche from occurrence records. We modeled separately the distributions of males and females, assuming records of females probably represented established home ranges while male records likely included dispersal...

Flood Frequency Curves - Use of information on the likelihood of extreme floods

NASA Astrophysics Data System (ADS)

Faber, B.

2011-12-01

Investment in the infrastructure that reduces flood risk for flood-prone communities must incorporate information on the magnitude and frequency of flooding in that area. Traditionally, that information has been a probability distribution of annual maximum streamflows developed from the historical gaged record at a stream site. Practice in the United States fits a Log-Pearson type3 distribution to the annual maximum flows of an unimpaired streamflow record, using the method of moments to estimate distribution parameters. The procedure makes the assumptions that annual peak streamflow events are (1) independent, (2) identically distributed, and (3) form a representative sample of the overall probability distribution. Each of these assumptions can be challenged. We rarely have enough data to form a representative sample, and therefore must compute and display the uncertainty in the estimated flood distribution. But, is there a wet/dry cycle that makes precipitation less than independent between successive years? Are the peak flows caused by different types of events from different statistical populations? How does the watershed or climate changing over time (non-stationarity) affect the probability distribution floods? Potential approaches to avoid these assumptions vary from estimating trend and shift and removing them from early data (and so forming a homogeneous data set), to methods that estimate statistical parameters that vary with time. A further issue in estimating a probability distribution of flood magnitude (the flood frequency curve) is whether a purely statistical approach can accurately capture the range and frequency of floods that are of interest. A meteorologically-based analysis produces "probable maximum precipitation" (PMP) and subsequently a "probable maximum flood" (PMF) that attempts to describe an upper bound on flood magnitude in a particular watershed. This analysis can help constrain the upper tail of the probability distribution, well beyond the range of gaged data or even historical or paleo-flood data, which can be very important in risk analyses performed for flood risk management and dam and levee safety studies.

The Cumulative Probability of Arrest by Age 28 Years in the United States by Disability Status, Race/Ethnicity, and Gender.

PubMed

McCauley, Erin J

2017-12-01

To estimate the cumulative probability (c) of arrest by age 28 years in the United States by disability status, race/ethnicity, and gender. I estimated cumulative probabilities through birth cohort life tables with data from the National Longitudinal Survey of Youth, 1997. Estimates demonstrated that those with disabilities have a higher cumulative probability of arrest (c = 42.65) than those without (c = 29.68). The risk was disproportionately spread across races/ethnicities, with Blacks with disabilities experiencing the highest cumulative probability of arrest (c = 55.17) and Whites without disabilities experiencing the lowest (c = 27.55). Racial/ethnic differences existed by gender as well. There was a similar distribution of disability types across race/ethnicity, suggesting that the racial/ethnic differences in arrest may stem from racial/ethnic inequalities as opposed to differential distribution of disability types. The experience of arrest for those with disabilities was higher than expected. Police officers should understand how disabilities may affect compliance and other behaviors, and likewise how implicit bias and structural racism may affect reactions and actions of officers and the systems they work within in ways that create inequities.

Modeling Uncertainty in Military Supply Chain Management Decisions

DTIC Science & Technology

2014-06-23

a compound probability distribution (Eppen and Martin, 1988; Lau and Lau , 2003; Lin, 2008). This paper will incorporate the previously described...distribution with and is selected for the regular state and the N (0.27,0.19) is chosen for state 2. The demand in each state for a given lead...supplier receives orders of size Q from the buyer and purchases inventory from its vendors in a quantity that is an integer multiple N of the buyer’s

Tree mortality estimates and species distribution probabilities in southeastern United States forests

Treesearch

Martin A. Spetich; Zhaofei Fan; Zhen Sui; Michael Crosby; Hong S. He; Stephen R. Shifley; Theodor D. Leininger; W. Keith Moser

2017-01-01

Stresses to trees under a changing climate can lead to changes in forest tree survival, mortality and distribution.  For instance, a study examining the effects of human-induced climate change on forest biodiversity by Hansen and others (2001) predicted a 32% reduction in loblolly–shortleaf pine habitat across the eastern United States.  However, they also...

A System-Level Throughput Model for Quantum Key Distribution

DTIC Science & Technology

2015-09-17

object. In quantum entanglement , the physical properties of particle pairs or groups of particles are correlated – the quantum state of each particle...One-Time Pad Algorithm ............................................................................. 8 Figure 2. Photon Polarization [19...64 Poisson distribution for multi- photon probability (29

Threshold-selecting strategy for best possible ground state detection with genetic algorithms

NASA Astrophysics Data System (ADS)

Lässig, Jörg; Hoffmann, Karl Heinz

2009-04-01

Genetic algorithms are a standard heuristic to find states of low energy in complex state spaces as given by physical systems such as spin glasses but also in combinatorial optimization. The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover. Many schemes have been considered in literature as possible crossover selection strategies. We show for a large class of quality measures that the best possible probability distribution for selecting individuals in each generation of the algorithm execution is a rectangular distribution over the individuals sorted by their energy values. This means uniform probabilities have to be assigned to a group of the individuals with lowest energy in the population but probabilities equal to zero to individuals which are corresponding to energy values higher than a fixed cutoff, which is equal to a certain rank in the vector sorted by the energy of the states in the current population. The considered strategy is dubbed threshold selecting. The proof applies basic arguments of Markov chains and linear optimization and makes only a few assumptions on the underlying principles and hence applies to a large class of algorithms.

Real-Time Safety Monitoring and Prediction for the National Airspace System

NASA Technical Reports Server (NTRS)

Roychoudhury, Indranil

2016-01-01

As new operational paradigms and additional aircraft are being introduced into the National Airspace System (NAS), maintaining safety in such a rapidly growing environment becomes more challenging. It is therefore desirable to have both an overview of the current safety of the airspace at different levels of granularity, as well an understanding of how the state of the safety will evolve into the future given the anticipated flight plans, weather forecasts, predicted health of assets in the airspace, and so on. To this end, we have developed a Real-Time Safety Monitoring (RTSM) that first, estimates the state of the NAS using the dynamic models. Then, given the state estimate and a probability distribution of future inputs to the NAS, the framework predicts the evolution of the NAS, i.e., the future state, and analyzes these future states to predict the occurrence of unsafe events. The entire probability distribution of airspace safety metrics is computed, not just point estimates, without significant assumptions regarding the distribution type and or parameters. We demonstrate our overall approach by predicting the occurrence of some unsafe events and show how these predictions evolve in time as flight operations progress.

Modeling and mapping the probability of occurrence of invasive wild pigs across the contiguous United States.

PubMed

McClure, Meredith L; Burdett, Christopher L; Farnsworth, Matthew L; Lutman, Mark W; Theobald, David M; Riggs, Philip D; Grear, Daniel A; Miller, Ryan S

2015-01-01

Wild pigs (Sus scrofa), also known as wild swine, feral pigs, or feral hogs, are one of the most widespread and successful invasive species around the world. Wild pigs have been linked to extensive and costly agricultural damage and present a serious threat to plant and animal communities due to their rooting behavior and omnivorous diet. We modeled the current distribution of wild pigs in the United States to better understand the physiological and ecological factors that may determine their invasive potential and to guide future study and eradication efforts. Using national-scale wild pig occurrence data reported between 1982 and 2012 by wildlife management professionals, we estimated the probability of wild pig occurrence across the United States using a logistic discrimination function and environmental covariates hypothesized to influence the distribution of the species. Our results suggest the distribution of wild pigs in the U.S. was most strongly limited by cold temperatures and availability of water, and that they were most likely to occur where potential home ranges had higher habitat heterogeneity, providing access to multiple key resources including water, forage, and cover. High probability of occurrence was also associated with frequent high temperatures, up to a high threshold. However, this pattern is driven by pigs' historic distribution in warm climates of the southern U.S. Further study of pigs' ability to persist in cold northern climates is needed to better understand whether low temperatures actually limit their distribution. Our model highlights areas at risk of invasion as those with habitat conditions similar to those found in pigs' current range that are also near current populations. This study provides a macro-scale approach to generalist species distribution modeling that is applicable to other generalist and invasive species.

Convergence of Transition Probability Matrix in CLVMarkov Models

NASA Astrophysics Data System (ADS)

Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.

2018-04-01

A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.

Attention as Inference: Selection Is Probabilistic; Responses Are All-or-None Samples

ERIC Educational Resources Information Center

Vul, Edward; Hanus, Deborah; Kanwisher, Nancy

2009-01-01

Theories of probabilistic cognition postulate that internal representations are made up of multiple simultaneously held hypotheses, each with its own probability of being correct (henceforth, "probability distributions"). However, subjects make discrete responses and report the phenomenal contents of their mind to be all-or-none states rather than…

Two-mode mazer injected with V-type three-level atoms

NASA Astrophysics Data System (ADS)

Liang, Wen-Qing; Zhang, Zhi-Ming; Xie, Sheng-Wu

2003-12-01

The properties of the two-mode mazer operating on V-type three-level atoms are studied. The effect of the one-atom pumping on the two modes of the cavity field in number-state is asymmetric, that is, the atom emits a photon into one mode with some probability and absorbs a photon from the other mode with some other probability. This effect makes the steady-state photon distribution and the steady-state photon statistics asymmetric for the two modes. The diagram of the probability currents for the photon distribution, given by the analysis of the master equation, reveals that there is no detailed balance solution for the master equation. The computations show that the photon statistics of one mode or both modes can be sub-Poissonian, that the two modes can have anticorrelation or correlation, that the photon statistics increases with the increase of thermal photons and that the resonant position and strength of the photon statistics are influenced by the ratio of the two coupling strengths of the two modes. These properties are also discussed physically.

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

Sampaio, R.; Suomela, S.; Ala-Nissila, T.; Anders, J.; Philbin, T. G.

2018-01-01

At nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory

NASA Astrophysics Data System (ADS)

Alvarez, Diego A.; Uribe, Felipe; Hurtado, Jorge E.

2018-02-01

Random set theory is a general framework which comprises uncertainty in the form of probability boxes, possibility distributions, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition, the dependence between the input variables can be expressed using copulas. In this paper, the lower and upper bounds on the probability of failure are calculated by means of random set theory. In order to accelerate the calculation, a well-known and efficient probability-based reliability method known as subset simulation is employed. This method is especially useful for finding small failure probabilities in both low- and high-dimensional spaces, disjoint failure domains and nonlinear limit state functions. The proposed methodology represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. Numerical examples illustrate the efficiency of the proposed approach.

Modeling highway travel time distribution with conditional probability models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira Neto, Francisco Moraes; Chin, Shih-Miao; Hwang, Ho-Ling

ABSTRACT Under the sponsorship of the Federal Highway Administration's Office of Freight Management and Operations, the American Transportation Research Institute (ATRI) has developed performance measures through the Freight Performance Measures (FPM) initiative. Under this program, travel speed information is derived from data collected using wireless based global positioning systems. These telemetric data systems are subscribed and used by trucking industry as an operations management tool. More than one telemetric operator submits their data dumps to ATRI on a regular basis. Each data transmission contains truck location, its travel time, and a clock time/date stamp. Data from the FPM program providesmore » a unique opportunity for studying the upstream-downstream speed distributions at different locations, as well as different time of the day and day of the week. This research is focused on the stochastic nature of successive link travel speed data on the continental United States Interstates network. Specifically, a method to estimate route probability distributions of travel time is proposed. This method uses the concepts of convolution of probability distributions and bivariate, link-to-link, conditional probability to estimate the expected distributions for the route travel time. Major contribution of this study is the consideration of speed correlation between upstream and downstream contiguous Interstate segments through conditional probability. The established conditional probability distributions, between successive segments, can be used to provide travel time reliability measures. This study also suggests an adaptive method for calculating and updating route travel time distribution as new data or information is added. This methodology can be useful to estimate performance measures as required by the recent Moving Ahead for Progress in the 21st Century Act (MAP 21).« less

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

Fingerprint Recognition with Identical Twin Fingerprints

PubMed Central

Yang, Xin; Tian, Jie

2012-01-01

Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar. PMID:22558204

Fingerprint recognition with identical twin fingerprints.

PubMed

Tao, Xunqiang; Chen, Xinjian; Yang, Xin; Tian, Jie

2012-01-01

Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar.

21 CFR 130.17 - Temporary permits for interstate shipment of experimental packs of food varying from the...

Code of Federal Regulations, 2011 CFR

2011-04-01

... Section 130.17 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES... provided. (11) The probable amount of such food that will be distributed. The amount distributed should be... distributed in the State in which it was manufactured. (15) If it has not been or is not to be so distributed...

21 CFR 130.17 - Temporary permits for interstate shipment of experimental packs of food varying from the...

Code of Federal Regulations, 2010 CFR

2010-04-01

... Section 130.17 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES... provided. (11) The probable amount of such food that will be distributed. The amount distributed should be... distributed in the State in which it was manufactured. (15) If it has not been or is not to be so distributed...

ON CONTINUOUS-REVIEW (S-1,S) INVENTORY POLICIES WITH STATE-DEPENDENT LEADTIMES,

DTIC Science & Technology

INVENTORY CONTROL, *REPLACEMENT THEORY), MATHEMATICAL MODELS, LEAD TIME , MANAGEMENT ENGINEERING, DISTRIBUTION FUNCTIONS, PROBABILITY, QUEUEING THEORY, COSTS, OPTIMIZATION, STATISTICAL PROCESSES, DIFFERENCE EQUATIONS

Moving on From Representativeness: Testing the Utility of the Global Drug Survey.

PubMed

Barratt, Monica J; Ferris, Jason A; Zahnow, Renee; Palamar, Joseph J; Maier, Larissa J; Winstock, Adam R

2017-01-01

A decline in response rates in traditional household surveys, combined with increased internet coverage and decreased research budgets, has resulted in increased attractiveness of web survey research designs based on purposive and voluntary opt-in sampling strategies. In the study of hidden or stigmatised behaviours, such as cannabis use, web survey methods are increasingly common. However, opt-in web surveys are often heavily criticised due to their lack of sampling frame and unknown representativeness. In this article, we outline the current state of the debate about the relevance of pursuing representativeness, the state of probability sampling methods, and the utility of non-probability, web survey methods especially for accessing hidden or minority populations. Our article has two aims: (1) to present a comprehensive description of the methodology we use at Global Drug Survey (GDS), an annual cross-sectional web survey and (2) to compare the age and sex distributions of cannabis users who voluntarily completed (a) a household survey or (b) a large web-based purposive survey (GDS), across three countries: Australia, the United States, and Switzerland. We find that within each set of country comparisons, the demographic distributions among recent cannabis users are broadly similar, demonstrating that the age and sex distributions of those who volunteer to be surveyed are not vastly different between these non-probability and probability methods. We conclude that opt-in web surveys of hard-to-reach populations are an efficient way of gaining in-depth understanding of stigmatised behaviours and are appropriate, as long as they are not used to estimate drug use prevalence of the general population.

Moving on From Representativeness: Testing the Utility of the Global Drug Survey

PubMed Central

Barratt, Monica J; Ferris, Jason A; Zahnow, Renee; Palamar, Joseph J; Maier, Larissa J; Winstock, Adam R

2017-01-01

A decline in response rates in traditional household surveys, combined with increased internet coverage and decreased research budgets, has resulted in increased attractiveness of web survey research designs based on purposive and voluntary opt-in sampling strategies. In the study of hidden or stigmatised behaviours, such as cannabis use, web survey methods are increasingly common. However, opt-in web surveys are often heavily criticised due to their lack of sampling frame and unknown representativeness. In this article, we outline the current state of the debate about the relevance of pursuing representativeness, the state of probability sampling methods, and the utility of non-probability, web survey methods especially for accessing hidden or minority populations. Our article has two aims: (1) to present a comprehensive description of the methodology we use at Global Drug Survey (GDS), an annual cross-sectional web survey and (2) to compare the age and sex distributions of cannabis users who voluntarily completed (a) a household survey or (b) a large web-based purposive survey (GDS), across three countries: Australia, the United States, and Switzerland. We find that within each set of country comparisons, the demographic distributions among recent cannabis users are broadly similar, demonstrating that the age and sex distributions of those who volunteer to be surveyed are not vastly different between these non-probability and probability methods. We conclude that opt-in web surveys of hard-to-reach populations are an efficient way of gaining in-depth understanding of stigmatised behaviours and are appropriate, as long as they are not used to estimate drug use prevalence of the general population. PMID:28924351

A quantum anharmonic oscillator model for the stock market

NASA Astrophysics Data System (ADS)

Gao, Tingting; Chen, Yu

2017-02-01

A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.

Force Transmission Modes of Non-Cohesive and Cohesive Materials at the Critical State.

PubMed

Wang, Ji-Peng

2017-08-31

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples.

Force Transmission Modes of Non-Cohesive and Cohesive Materials at the Critical State

PubMed Central

2017-01-01

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples. PMID:28858238

A Financial Market Model Incorporating Herd Behaviour

PubMed Central

2016-01-01

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option. PMID:27007236

Robust state transfer in the quantum spin channel via weak measurement and quantum measurement reversal

NASA Astrophysics Data System (ADS)

He, Zhi; Yao, Chunmei; Zou, Jian

2013-10-01

Using the weak measurement (WM) and quantum measurement reversal (QMR) approach, robust state transfer and entanglement distribution can be realized in the spin-(1)/(2) Heisenberg chain. We find that the ultrahigh fidelity and long distance of quantum state transfer with certain success probability can be obtained using proper WM and QMR, i.e., the average fidelity of a general pure state from 80% to almost 100%, which is almost size independent. We also find that the distance and quality of entanglement distribution for the Bell state and the general Werner mixed state can be obviously improved by the WM and QMR approach.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Role of conviction in nonequilibrium models of opinion formation

NASA Astrophysics Data System (ADS)

Crokidakis, Nuno; Anteneodo, Celia

2012-12-01

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value (±1 or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability p (1-p), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point pc that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

Relaxation of ferroelectric states in 2D distributions of quantum dots: EELS simulation

NASA Astrophysics Data System (ADS)

Cortés, C. M.; Meza-Montes, L.; Moctezuma, R. E.; Carrillo, J. L.

2016-06-01

The relaxation time of collective electronic states in a 2D distribution of quantum dots is investigated theoretically by simulating EELS experiments. From the numerical calculation of the probability of energy loss of an electron beam, traveling parallel to the distribution, it is possible to estimate the damping time of ferroelectric-like states. We generate this collective response of the distribution by introducing a mean field interaction among the quantum dots, and then, the model is extended incorporating effects of long-range correlations through a Bragg-Williams approximation. The behavior of the dielectric function, the energy loss function, and the relaxation time of ferroelectric-like states is then investigated as a function of the temperature of the distribution and the damping constant of the electronic states in the single quantum dots. The robustness of the trends and tendencies of our results indicate that this scheme of analysis can guide experimentalists to develop tailored quantum dots distributions for specific applications.

Probability Forecasting Using Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Duncan, M.; Frisbee, J.; Wysack, J.

2014-09-01

Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a collision probability distribution given known, predicted uncertainty. This paper presents the details of the collision probability forecasting method. We examine various conjunction event scenarios and numerically demonstrate the utility of this approach in typical event scenarios. We explore the utility of a probability-based track scenario simulation that models expected tracking data frequency as the tasking levels are increased. The resulting orbital uncertainty is subsequently used in the forecasting algorithm.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

Rogue waves driven by polarization instabilities in a long ring fiber oscillator

NASA Astrophysics Data System (ADS)

Kolpakov, S. A.; Kbashi, Hani; Sergeyev, Sergey

2017-05-01

We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1989-01-01

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Continental-scale simulation of burn probabilities, flame lengths, and fire size distribution for the United States

Treesearch

Mark A. Finney; Charles W. McHugh; Isaac Grenfell; Karin L. Riley

2010-01-01

Components of a quantitative risk assessment were produced by simulation of burn probabilities and fire behavior variation for 134 fire planning units (FPUs) across the continental U.S. The system uses fire growth simulation of ignitions modeled from relationships between large fire occurrence and the fire danger index Energy Release Component (ERC). Simulations of 10,...

On the Structure of a Best Possible Crossover Selection Strategy in Genetic Algorithms

NASA Astrophysics Data System (ADS)

Lässig, Jörg; Hoffmann, Karl Heinz

The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to find a solution with high fitness for a given optimization problem. Many different schemes have been described in the literature as possible strategies for this task but so far comparisons have been predominantly empirical. It is shown that if one wishes to maximize any linear function of the final state probabilities, e.g. the fitness of the best individual in the final population of the algorithm, then a best probability distribution for selecting an individual in each generation is a rectangular distribution over the individuals sorted in descending sequence by their fitness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals with lower fitness, assuming that the probability distribution to choose individuals from the current population can be chosen independently for each iteration and each individual. This result is then generalized also to typical practically applied performance measures, such as maximizing the expected fitness value of the best individual seen in any generation.

Conditional Probabilities and Collapse in Quantum Measurements

NASA Astrophysics Data System (ADS)

Laura, Roberto; Vanni, Leonardo

2008-09-01

We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a measurement with a given result, which gives the probability distribution for all possible consecutive measurements on the system. This statistical operator, representing the state of the system after the first measurement, is in general not the same that would be obtained using the postulate of collapse.

Using type IV Pearson distribution to calculate the probabilities of underrun and overrun of lists of multiple cases.

PubMed

Wang, Jihan; Yang, Kai

2014-07-01

An efficient operating room needs both little underutilised and overutilised time to achieve optimal cost efficiency. The probabilities of underrun and overrun of lists of cases can be estimated by a well defined duration distribution of the lists. To propose a method of predicting the probabilities of underrun and overrun of lists of cases using Type IV Pearson distribution to support case scheduling. Six years of data were collected. The first 5 years of data were used to fit distributions and estimate parameters. The data from the last year were used as testing data to validate the proposed methods. The percentiles of the duration distribution of lists of cases were calculated by Type IV Pearson distribution and t-distribution. Monte Carlo simulation was conducted to verify the accuracy of percentiles defined by the proposed methods. Operating rooms in John D. Dingell VA Medical Center, United States, from January 2005 to December 2011. Differences between the proportion of lists of cases that were completed within the percentiles of the proposed duration distribution of the lists and the corresponding percentiles. Compared with the t-distribution, the proposed new distribution is 8.31% (0.38) more accurate on average and 14.16% (0.19) more accurate in calculating the probabilities at the 10th and 90th percentiles of the distribution, which is a major concern of operating room schedulers. The absolute deviations between the percentiles defined by Type IV Pearson distribution and those from Monte Carlo simulation varied from 0.20  min (0.01) to 0.43  min (0.03). Operating room schedulers can rely on the most recent 10 cases with the same combination of surgeon and procedure(s) for distribution parameter estimation to plan lists of cases. Values are mean (SEM). The proposed Type IV Pearson distribution is more accurate than t-distribution to estimate the probabilities of underrun and overrun of lists of cases. However, as not all the individual case durations followed log-normal distributions, there was some deviation from the true duration distribution of the lists.

Quantitative prediction of collision-induced vibration-rotation distributions from physical data

NASA Astrophysics Data System (ADS)

Marsh, Richard J.; McCaffery, Anthony J.

2003-04-01

We describe a rapid, accurate technique for computing state-to-state cross-sections in collision-induced vibration-rotation transfer (VRT) using only physical data, i.e. spectroscopic constants, bond length, mass and velocity distribution. The probability of linear-to-angular momentum (AM) conversion is calculated for a set of trajectories, each of which is subjected to energy conservation boundary conditions. No mechanism is specified for inducing vibrational state change. In the model, this constitutes a velocity or momentum barrier that must be overcome before rotational AM may be generated in the new vibrational state. The method is subjected to stringent testing by calculating state-to-state VRT probabilities for diatomics in highly excited vibrational, rotational and electronic states. Comparison is made to experimental data and to results from quantum mechanical and from quasi-classical trajectory calculations. There is quantitative agreement with data from all three sources, indicating that despite its simplicity the essential physics of collisions involving highly excited species is captured in the model. We develop further the concept of the molecular efficiency factor as an indicative parameter in collision dynamics, and derive an expression for ji > 0 and for VRT.

A Probabilistic Framework for Quantifying Mixed Uncertainties in Cyber Attacker Payoffs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Samrat; Tipireddy, Ramakrishna; Oster, Matthew R.

Quantification and propagation of uncertainties in cyber attacker payoffs is a key aspect within multiplayer, stochastic security games. These payoffs may represent penalties or rewards associated with player actions and are subject to various sources of uncertainty, including: (1) cyber-system state, (2) attacker type, (3) choice of player actions, and (4) cyber-system state transitions over time. Past research has primarily focused on representing defender beliefs about attacker payoffs as point utility estimates. More recently, within the physical security domain, attacker payoff uncertainties have been represented as Uniform and Gaussian probability distributions, and mathematical intervals. For cyber-systems, probability distributions may helpmore » address statistical (aleatory) uncertainties where the defender may assume inherent variability or randomness in the factors contributing to the attacker payoffs. However, systematic (epistemic) uncertainties may exist, where the defender may not have sufficient knowledge or there is insufficient information about the attacker’s payoff generation mechanism. Such epistemic uncertainties are more suitably represented as generalizations of probability boxes. This paper explores the mathematical treatment of such mixed payoff uncertainties. A conditional probabilistic reasoning approach is adopted to organize the dependencies between a cyber-system’s state, attacker type, player actions, and state transitions. This also enables the application of probabilistic theories to propagate various uncertainties in the attacker payoffs. An example implementation of this probabilistic framework and resulting attacker payoff distributions are discussed. A goal of this paper is also to highlight this uncertainty quantification problem space to the cyber security research community and encourage further advancements in this area.« less

On the probability distribution of daily streamflow in the United States

USGS Publications Warehouse

Blum, Annalise G.; Archfield, Stacey A.; Vogel, Richard M.

2017-01-01

Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.

Quantum Jeffreys prior for displaced squeezed thermal states

NASA Astrophysics Data System (ADS)

Kwek, L. C.; Oh, C. H.; Wang, Xiang-Bin

1999-09-01

It is known that, by extending the equivalence of the Fisher information matrix to its quantum version, the Bures metric, the quantum Jeffreys prior can be determined from the volume element of the Bures metric. We compute the Bures metric for the displaced squeezed thermal state and analyse the quantum Jeffreys prior and its marginal probability distributions. To normalize the marginal probability density function, it is necessary to provide a range of values of the squeezing parameter or the inverse temperature. We find that if the range of the squeezing parameter is kept narrow, there are significant differences in the marginal probability density functions in terms of the squeezing parameters for the displaced and undisplaced situations. However, these differences disappear as the range increases. Furthermore, marginal probability density functions against temperature are very different in the two cases.

Calibration of micromechanical parameters for DEM simulations by using the particle filter

NASA Astrophysics Data System (ADS)

Cheng, Hongyang; Shuku, Takayuki; Thoeni, Klaus; Yamamoto, Haruyuki

2017-06-01

The calibration of DEM models is typically accomplished by trail and error. However, the procedure lacks of objectivity and has several uncertainties. To deal with these issues, the particle filter is employed as a novel approach to calibrate DEM models of granular soils. The posterior probability distribution of the microparameters that give numerical results in good agreement with the experimental response of a Toyoura sand specimen is approximated by independent model trajectories, referred as `particles', based on Monte Carlo sampling. The soil specimen is modeled by polydisperse packings with different numbers of spherical grains. Prepared in `stress-free' states, the packings are subjected to triaxial quasistatic loading. Given the experimental data, the posterior probability distribution is incrementally updated, until convergence is reached. The resulting `particles' with higher weights are identified as the calibration results. The evolutions of the weighted averages and posterior probability distribution of the micro-parameters are plotted to show the advantage of using a particle filter, i.e., multiple solutions are identified for each parameter with known probabilities of reproducing the experimental response.

Complex growing networks with intrinsic vertex fitness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bedogne, C.; Rodgers, G. J.

2006-10-15

One of the major questions in complex network research is to identify the range of mechanisms by which a complex network can self organize into a scale-free state. In this paper we investigate the interplay between a fitness linking mechanism and both random and preferential attachment. In our models, each vertex is assigned a fitness x, drawn from a probability distribution {rho}(x). In Model A, at each time step a vertex is added and joined to an existing vertex, selected at random, with probability p and an edge is introduced between vertices with fitnesses x and y, with a ratemore » f(x,y), with probability 1-p. Model B differs from Model A in that, with probability p, edges are added with preferential attachment rather than randomly. The analysis of Model A shows that, for every fixed fitness x, the network's degree distribution decays exponentially. In Model B we recover instead a power-law degree distribution whose exponent depends only on p, and we show how this result can be generalized. The properties of a number of particular networks are examined.« less

Dynamical complexity changes during two forms of meditation

NASA Astrophysics Data System (ADS)

Li, Jin; Hu, Jing; Zhang, Yinhong; Zhang, Xiaofeng

2011-06-01

Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.

Scattering of 42 MeV alpha particles from copper-65

NASA Technical Reports Server (NTRS)

Stewart, W. M.; Seth, K. K.

1973-01-01

Beams of 42-MeV alpha particles were elastically and inelastically scattered from Cu-65 in an attempt to excite states which may be described in terms of an excited core model. Angular distributions were measured for 17 excited states. Seven of the excited states had angular distributions similar to a core quadrupole excitation and eight of the excited states had angular distributions similar to a core octupole excitation. The excited state at 2.858 MeV had an angular distribution which suggests that it may have results from the particle coupling to a two-phonon core state. An extended particle-core coupling calculation was performed and the predicted energy levels and reduced transition probabilities compared to the experimental data. The low lying levels are described quite well and the wavefunctions of these states explain the large spectroscopic factors measured in stripping reactions. For Cu-65 the coupling of the particle to the core is no larger weak as in the simpler model, and configuration mixing results.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

Identifying early-warning signals of critical transitions with strong noise by dynamical network markers

PubMed Central

Liu, Rui; Chen, Pei; Aihara, Kazuyuki; Chen, Luonan

2015-01-01

Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: “making big noise smaller” by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher-dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher-dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems. PMID:26647650

Empirical models of transitions between coral reef states: effects of region, protection, and environmental change.

PubMed

Lowe, Phillip K; Bruno, John F; Selig, Elizabeth R; Spencer, Matthew

2011-01-01

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions. We analyzed reef surveys from the Caribbean and GBR (1996-2006). We defined a set of reef states distinguished by coral and macroalgal cover, and obtained Bayesian estimates of the annual probabilities of transitions between these states. The Caribbean and GBR had different transition probabilities, and therefore different rates of change in reef condition. This could be due to differences in species composition, management or the nature and extent of disturbances between these regions. We then estimated equilibrium probability distributions for reef states, and coral and macroalgal cover under constant environmental conditions. In both regions, the current distributions are close to equilibrium. In the Caribbean, coral cover is much lower and macroalgal cover is higher at equilibrium than in the GBR. We found no evidence for differences in transition probabilities between the first and second halves of our survey period, or between Caribbean reefs inside and outside marine protected areas. However, our power to detect such differences may have been low. We also examined the effects of altering transition probabilities on the community state equilibrium, along a continuum from unfavourable (e.g., increased sea surface temperature) to favourable (e.g., improved management) conditions. Both regions showed similar qualitative responses, but different patterns of uncertainty. In the Caribbean, uncertainty was greatest about effects of favourable changes, while in the GBR, we are most uncertain about effects of unfavourable changes. Our approach could be extended to provide risk analysis for management decisions.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

A scaling law for random walks on networks

PubMed Central

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-01-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

A scaling law for random walks on networks

NASA Astrophysics Data System (ADS)

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A scaling law for random walks on networks.

PubMed

Perkins, Theodore J; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-14

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

Superthermal photon bunching in terms of simple probability distributions

NASA Astrophysics Data System (ADS)

Lettau, T.; Leymann, H. A. M.; Melcher, B.; Wiersig, J.

2018-05-01

We analyze the second-order photon autocorrelation function g(2 ) with respect to the photon probability distribution and discuss the generic features of a distribution that results in superthermal photon bunching [g(2 )(0 ) >2 ]. Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes such as superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy if only the intensity and the second-order autocorrelation are given. However, for bimodal systems, an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasinglike state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, i.e., a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore, the excellent agreement of the statistics of the bimodal laser and our model reveals that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.

On the continuity of the stationary state distribution of DPCM

NASA Astrophysics Data System (ADS)

Naraghi-Pour, Morteza; Neuhoff, David L.

1990-03-01

Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e., delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediciton coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e., it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e., either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Efficient quantum repeater with respect to both entanglement-concentration rate and complexity of local operations and classical communication

NASA Astrophysics Data System (ADS)

Su, Zhaofeng; Guan, Ji; Li, Lvzhou

2018-01-01

Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, in practice, it is difficult to distribute quantum entanglement over a long distance, due to the absorption and noise in quantum channels. A solution to this challenge is a quantum repeater, which can extend the distance of entanglement distribution. In this scheme, the time consumption of classical communication and local operations takes an important place with respect to time efficiency. Motivated by this observation, we consider a basic quantum repeater scheme that focuses on not only the optimal rate of entanglement concentration but also the complexity of local operations and classical communication. First, we consider the case where two different two-qubit pure states are initially distributed in the scenario. We construct a protocol with the optimal entanglement-concentration rate and less consumption of local operations and classical communication. We also find a criterion for the projective measurements to achieve the optimal probability of creating a maximally entangled state between the two ends. Second, we consider the case in which two general pure states are prepared and general measurements are allowed. We get an upper bound on the probability for a successful measurement operation to produce a maximally entangled state without any further local operations.

Intertime jump statistics of state-dependent Poisson processes.

PubMed

Daly, Edoardo; Porporato, Amilcare

2007-01-01

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

Effect of weak measurement on entanglement distribution over noisy channels.

PubMed

Wang, Xin-Wen; Yu, Sixia; Zhang, Deng-Yu; Oh, C H

2016-03-03

Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence.

Effect of weak measurement on entanglement distribution over noisy channels

PubMed Central

Wang, Xin-Wen; Yu, Sixia; Zhang, Deng-Yu; Oh, C. H.

2016-01-01

Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence. PMID:26935775

Direct calculation of liquid-vapor phase equilibria from transition matrix Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Errington, Jeffrey R.

2003-06-01

An approach for directly determining the liquid-vapor phase equilibrium of a model system at any temperature along the coexistence line is described. The method relies on transition matrix Monte Carlo ideas developed by Fitzgerald, Picard, and Silver [Europhys. Lett. 46, 282 (1999)]. During a Monte Carlo simulation attempted transitions between states along the Markov chain are monitored as opposed to tracking the number of times the chain visits a given state as is done in conventional simulations. Data collection is highly efficient and very precise results are obtained. The method is implemented in both the grand canonical and isothermal-isobaric ensemble. The main result from a simulation conducted at a given temperature is a density probability distribution for a range of densities that includes both liquid and vapor states. Vapor pressures and coexisting densities are calculated in a straightforward manner from the probability distribution. The approach is demonstrated with the Lennard-Jones fluid. Coexistence properties are directly calculated at temperatures spanning from the triple point to the critical point.

Self-organizing behavior in a lattice model for co-evolution of virus and immune systems

NASA Astrophysics Data System (ADS)

Izmailian, N. Sh.; Papoyan, Vl. V.; Priezzhev, V. B.; Hu, Chin-Kun

2007-04-01

We propose a lattice model for the co-evolution of a virus population and an adaptive immune system. We show that, under some natural assumptions, both probability distribution of the virus population and the distribution of activity of the immune system tend during the evolution to a self-organized critical state.

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.

PubMed

Namikawa, Jun

2005-08-01

Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

Continuous-variable quantum key distribution in uniform fast-fading channels

NASA Astrophysics Data System (ADS)

Papanastasiou, Panagiotis; Weedbrook, Christian; Pirandola, Stefano

2018-03-01

We investigate the performance of several continuous-variable quantum key distribution protocols in the presence of uniform fading channels. These are lossy channels whose transmissivity changes according to a uniform probability distribution. We assume the worst-case scenario where an eavesdropper induces a fast-fading process, where she chooses the instantaneous transmissivity while the remote parties may only detect the mean statistical effect. We analyze coherent-state protocols in various configurations, including the one-way switching protocol in reverse reconciliation, the measurement-device-independent protocol in the symmetric configuration, and its extension to a three-party network. We show that, regardless of the advantage given to the eavesdropper (control of the fading), these protocols can still achieve high rates under realistic attacks, within reasonable values for the variance of the probability distribution associated with the fading process.

Faithful Remote Information Concentration Based on the Optimal Universal 1→2 Telecloning of Arbitrary Two-Qubit States

NASA Astrophysics Data System (ADS)

Peng, Jia-Yin; Lei, Hong-Xuan; Mo, Zhi-Wen

2014-05-01

The previous protocols of remote quantum information concentration were focused on the reverse process of quantum telecloning of single-qubit states. We here investigate the reverse process of optimal universal 1→2 telecloning of arbitrary two-qubit states. The aim of this telecloning is to distribute respectively the quantum information to two groups of spatially separated receivers from a group of two senders situated at two different locations. Our scheme shows that the distributed quantum information can be remotely concentrated back to a group of two different receivers with 1 of probability by utilizing maximally four-particle cluster state and four-particle GHZ state as quantum channel.

MERCURY CONCENTRATION IN FISH FROM STREAMS AND RIVERS THROUGHOUT THE WESTERN UNITED STATES

EPA Science Inventory

We collected and analyzed 2,707 large fish from 626 stream/river sites in 12 western U.S. states using a probability design to assess the regional distribution of whole fish mercury (Hg) concentrations. Large (>120 mm total length) fish Hg levels were strongly related to both fis...

Anomalous dismeter distribution shifts estimated from FIA inventories through time

Treesearch

Francis A. Roesch; Paul C. Van Deusen

2010-01-01

In the past decade, the United States Department of Agriculture Forest Service’s Forest Inventory and Analysis Program (FIA) has replaced regionally autonomous, periodic, state-wide forest inventories using various probability proportional to tree size sampling designs with a nationally consistent annual forest inventory design utilizing systematically spaced clusters...

Optical Field-Strength Polarization of Two-Mode Single-Photon States

ERIC Educational Resources Information Center

Linares, J.; Nistal, M. C.; Barral, D.; Moreno, V.

2010-01-01

We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of…

Universality of optimal measurements

NASA Astrophysics Data System (ADS)

Tarrach, Rolf; Vidal, Guifré

1999-11-01

We present optimal and minimal measurements on identical copies of an unknown state of a quantum bit when the quality of measuring strategies is quantified with the gain of information (Kullback-or mutual information-of probability distributions). We also show that the maximal gain of information occurs, among isotropic priors, when the state is known to be pure. Universality of optimal measurements follows from our results: using the fidelity or the gain of information, two different figures of merits, leads to exactly the same conclusions for isotropic distributions. We finally investigate the optimal capacity of N copies of an unknown state as a quantum channel of information.

Mathematical Analysis of Vehicle Delivery Scale of Bike-Sharing Rental Nodes

NASA Astrophysics Data System (ADS)

Zhai, Y.; Liu, J.; Liu, L.

2018-04-01

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

Skill of Ensemble Seasonal Probability Forecasts

NASA Astrophysics Data System (ADS)

Smith, Leonard A.; Binter, Roman; Du, Hailiang; Niehoerster, Falk

2010-05-01

In operational forecasting, the computational complexity of large simulation models is, ideally, justified by enhanced performance over simpler models. We will consider probability forecasts and contrast the skill of ENSEMBLES-based seasonal probability forecasts of interest to the finance sector (specifically temperature forecasts for Nino 3.4 and the Atlantic Main Development Region (MDR)). The ENSEMBLES model simulations will be contrasted against forecasts from statistical models based on the observations (climatological distributions) and empirical dynamics based on the observations but conditioned on the current state (dynamical climatology). For some start dates, individual ENSEMBLES models yield significant skill even at a lead-time of 14 months. The nature of this skill is discussed, and chances of application are noted. Questions surrounding the interpretation of probability forecasts based on these multi-model ensemble simulations are then considered; the distributions considered are formed by kernel dressing the ensemble and blending with the climatology. The sources of apparent (RMS) skill in distributions based on multi-model simulations is discussed, and it is demonstrated that the inclusion of "zero-skill" models in the long range can improve Root-Mean-Square-Error scores, casting some doubt on the common justification for the claim that all models should be included in forming an operational probability forecast. It is argued that the rational response varies with lead time.

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2017-02-01

The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of description of physical phenomena. In general there are no reasons to expect that properties of ontic states are approachable through our measurements. There is a gap between ontic and epistemic descriptions, cf. also with 't Hooft [49,50] and G G. Groessing et al. [51]. In general the presence of such a gap also implies unapproachability of the probabilistic ontic states, i.e., probability distributions on the space of ontic states. De Broglie [28] called such probability distributions hidden probabilities and distinguished them sharply from probability distributions of measurements outcomes, see also Lochak [29]. (The latter distributions are described by the quantum formalism.)This ontic-epistemic approach based on the combination of two descriptive levels for natural phenomena is closely related to the old Bild conception which was originated in the works of Hertz. Later it was heavily explored by Schrödinger in the quantum domain, see, e.g., [8,11] for detailed analysis. According to Hertz one cannot expect to construct a complete theoretical model based explicitly on observable quantities. The complete theoretical model can contain quantities which are unapproachable for external measurement inspection. For example, Hertz by trying to create a mechanical model for Maxwell's electromagnetism invented hidden masses. The main distinguishing property of a theoretical model (in contrast to an observational model) is the continuity of description, i.e., the absence of gaps in description. From this viewpoint, the quantum mechanical description is not continuous: there is a gap between premeasurement dynamics and the measurement outcome. QM cannot say anything what happens in the process of measurement, this is the well known measurement problem of QM [32], cf. [52,53]. Continuity of description is closely related to causality. However, here we cannot go in more detail, see [8,11].The important question is about interrelation between two levels of description, ontic-epistemic (or theoretical-observational). In the introduction we have already cited Schrödinger who emphasized the possible complexity of this interrelation. In particular, in general there is no reason to expect a straightforward coupling of the form, cf. [9,10]:

A moment-convergence method for stochastic analysis of biochemical reaction networks.

PubMed

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou

2016-05-21

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Decoy-state quantum key distribution with biased basis choice

PubMed Central

Wei, Zhengchao; Wang, Weilong; Zhang, Zhen; Gao, Ming; Ma, Zhi; Ma, Xiongfeng

2013-01-01

We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states. PMID:23948999

Decoy-state quantum key distribution with biased basis choice.

PubMed

Wei, Zhengchao; Wang, Weilong; Zhang, Zhen; Gao, Ming; Ma, Zhi; Ma, Xiongfeng

2013-01-01

We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states.

The estimated lifetime probability of acquiring human papillomavirus in the United States.

PubMed

Chesson, Harrell W; Dunne, Eileen F; Hariri, Susan; Markowitz, Lauri E

2014-11-01

Estimates of the lifetime probability of acquiring human papillomavirus (HPV) can help to quantify HPV incidence, illustrate how common HPV infection is, and highlight the importance of HPV vaccination. We developed a simple model, based primarily on the distribution of lifetime numbers of sex partners across the population and the per-partnership probability of acquiring HPV, to estimate the lifetime probability of acquiring HPV in the United States in the time frame before HPV vaccine availability. We estimated the average lifetime probability of acquiring HPV among those with at least 1 opposite sex partner to be 84.6% (range, 53.6%-95.0%) for women and 91.3% (range, 69.5%-97.7%) for men. Under base case assumptions, more than 80% of women and men acquire HPV by age 45 years. Our results are consistent with estimates in the existing literature suggesting a high lifetime probability of HPV acquisition and are supported by cohort studies showing high cumulative HPV incidence over a relatively short period, such as 3 to 5 years.

Can different quantum state vectors correspond to the same physical state? An experimental test

NASA Astrophysics Data System (ADS)

Nigg, Daniel; Monz, Thomas; Schindler, Philipp; Martinez, Esteban A.; Hennrich, Markus; Blatt, Rainer; Pusey, Matthew F.; Rudolph, Terry; Barrett, Jonathan

2016-01-01

A century after the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular quantum state vector, does this represent directly a physical property of the system, or is the state vector merely a summary of the physicist’s information about the system? Assume that a state vector corresponds to a probability distribution over possible values of an unknown physical or ‘ontic’ state. Then, a recent no-go theorem shows that distinct state vectors with overlapping distributions lead to predictions different from quantum theory. We report an experimental test of these predictions using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of models are ruled out.

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factor increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions constrained between the time axis and the exponential growth curve. Finally, since each lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Dynamical Response of Networks Under External Perturbations: Exact Results

NASA Astrophysics Data System (ADS)

Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.

2015-04-01

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.

Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

NASA Astrophysics Data System (ADS)

Etter, Tom; Noyes, H. Pierre

We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics.

PubMed

Ghavami, Siavash; Wolkenhauer, Olaf; Lahouti, Farshad; Ullah, Mukhtar; Linnebacher, Michael

2014-10-01

Knowing the expected temporal evolution of the proportion of different cell types in sample tissues gives an indication about the progression of the disease and its possible response to drugs. Such systems have been modelled using Markov processes. We here consider an experimentally realistic scenario in which transition probabilities are estimated from noisy cell population size measurements. Using aggregated data of FACS measurements, we develop MMSE and ML estimators and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes. Our numerical results show that the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach for noisy measurements. This provides support for our argument that for the analysis of FACS data one should consider the observed state as a random variable. The second problem we address is about the consequences of estimating the probability of a cell being in a particular state from measurements of small population of cells. We show how the uncertainty arising from small sample sizes can be captured by a distribution for the state probability.

Closed-form solution of decomposable stochastic models

NASA Technical Reports Server (NTRS)

Sjogren, Jon A.

1990-01-01

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Population Profile of the United States: 1976. Current Population Reports, Population Characteristics, Series P-20, No. 307.

ERIC Educational Resources Information Center

Bureau of the Census (DOC), Suitland, MD. Population Div.

This booklet summarizes population characteristics of the United States for 1976. A preliminary section of highlights reviews trends in five areas: population growth, social characteristics, population distribution, employment and income, and ethnic groups. The birth rate has declined, and the rate of childlessness has risen. This probably is due…

Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.

A statistical analysis of the daily streamflow hydrograph

NASA Astrophysics Data System (ADS)

Kavvas, M. L.; Delleur, J. W.

1984-03-01

In this study a periodic statistical analysis of daily streamflow data in Indiana, U.S.A., was performed to gain some new insight into the stochastic structure which describes the daily streamflow process. This analysis was performed by the periodic mean and covariance functions of the daily streamflows, by the time and peak discharge -dependent recession limb of the daily streamflow hydrograph, by the time and discharge exceedance level (DEL) -dependent probability distribution of the hydrograph peak interarrival time, and by the time-dependent probability distribution of the time to peak discharge. Some new statistical estimators were developed and used in this study. In general features, this study has shown that: (a) the persistence properties of daily flows depend on the storage state of the basin at the specified time origin of the flow process; (b) the daily streamflow process is time irreversible; (c) the probability distribution of the daily hydrograph peak interarrival time depends both on the occurrence time of the peak from which the inter-arrival time originates and on the discharge exceedance level; and (d) if the daily streamflow process is modeled as the release from a linear watershed storage, this release should depend on the state of the storage and on the time of the release as the persistence properties and the recession limb decay rates were observed to change with the state of the watershed storage and time. Therefore, a time-varying reservoir system needs to be considered if the daily streamflow process is to be modeled as the release from a linear watershed storage.

Computer Vision Tracking Using Particle Filters for 3D Position Estimation

DTIC Science & Technology

2014-03-27

the United States Air Force, the Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is...probability distribution (unless otherwise noted) π proposal distribution ω importance weight i index of normalized weights δ Dirac -delta function x...p(x) and the importance weights, where δ is the Dirac delta function [2, p. 178]. p(x) = N∑ n=1 ωnδ (x − xn) (2.14) ωn ∝ p(x) π(x) (2.15) Applying

Encounter risk analysis of rainfall and reference crop evapotranspiration in the irrigation district

NASA Astrophysics Data System (ADS)

Zhang, Jinping; Lin, Xiaomin; Zhao, Yong; Hong, Yang

2017-09-01

Rainfall and reference crop evapotranspiration are random but mutually affected variables in the irrigation district, and their encounter situation can determine water shortage risks under the contexts of natural water supply and demand. However, in reality, the rainfall and reference crop evapotranspiration may have different marginal distributions and their relations are nonlinear. In this study, based on the annual rainfall and reference crop evapotranspiration data series from 1970 to 2013 in the Luhun irrigation district of China, the joint probability distribution of rainfall and reference crop evapotranspiration are developed with the Frank copula function. Using the joint probability distribution, the synchronous-asynchronous encounter risk, conditional joint probability, and conditional return period of different combinations of rainfall and reference crop evapotranspiration are analyzed. The results show that the copula-based joint probability distributions of rainfall and reference crop evapotranspiration are reasonable. The asynchronous encounter probability of rainfall and reference crop evapotranspiration is greater than their synchronous encounter probability, and the water shortage risk associated with meteorological drought (i.e. rainfall variability) is more prone to appear. Compared with other states, there are higher conditional joint probability and lower conditional return period in either low rainfall or high reference crop evapotranspiration. For a specifically high reference crop evapotranspiration with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is increased with the decrease in frequency. For a specifically low rainfall with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is decreased with the decrease in frequency. When either the high reference crop evapotranspiration exceeds a certain frequency or low rainfall does not exceed a certain frequency, the higher conditional joint probability and lower conditional return period of various combinations likely cause a water shortage, but the water shortage is not severe.

The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korhonen, Marko; Lee, Eunghyun

2014-01-15

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle'smore » position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.« less

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Quantum squeezed state analysis of spontaneous ultra weak light photon emission of practitioners of meditation and control subjects.

PubMed

Van Wijk, Eduard P A; Van Wijk, Roeland; Bajpai, Rajendra P

2008-05-01

Research on human ultra-weak photon emission (UPE) has suggested a typical human emission anatomic percentage distribution pattern. It was demonstrated that emission intensities are lower in long-term practitioners of meditation as compared to control subjects. The percent contribution of emission from different anatomic locations was not significantly different for meditation practitioners and control subjects. Recently, a procedure was developed to analyze the fluctuations in the signals by measuring probabilities of detecting different numbers of photons in a bin and correct these for background noise. The procedure was tested utilizing the signal from three different body locations of a single subject, demonstrating that probabilities have non-classical features and are well described by the signal in a coherent state from the three body sites. The values indicate that the quantum state of photon emitted by the subject could be a coherent state in the subject being investigated. The objective in the present study was to systematically quantify, in subjects with long-term meditation experience and subjects without this experience, the photon count distribution of 12 different locations. Data show a variation in quantum state parameters within each individual subject as well as variation in quantum state parameters between the groups.

Epidemic extinction paths in complex networks

NASA Astrophysics Data System (ADS)

Hindes, Jason; Schwartz, Ira B.

2017-05-01

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

Epidemic extinction paths in complex networks.

PubMed

Hindes, Jason; Schwartz, Ira B

2017-05-01

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

Distribution of G concurrence of random pure states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol

2006-12-15

The average entanglement of random pure states of an NxN composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant, we characterize the probability distribution P(D). Similar results are obtained for the rescaled Nth root of the determinant, called the G concurrence. We show that in the limit N{yields}{infinity} this quantity becomes concentrated at a single point G{sub *}=1/e. The position of the concentration point changes if one consider an arbitrary NxK bipartite system, in the joint limit N,K{yields}{infinity}, with K/N fixed.

Precipitation intensity probability distribution modelling for hydrological and construction design purposes

NASA Astrophysics Data System (ADS)

Koshinchanov, Georgy; Dimitrov, Dobri

2008-11-01

The characteristics of rainfall intensity are important for many purposes, including design of sewage and drainage systems, tuning flood warning procedures, etc. Those estimates are usually statistical estimates of the intensity of precipitation realized for certain period of time (e.g. 5, 10 min., etc) with different return period (e.g. 20, 100 years, etc). The traditional approach in evaluating the mentioned precipitation intensities is to process the pluviometer's records and fit probability distribution to samples of intensities valid for certain locations ore regions. Those estimates further become part of the state regulations to be used for various economic activities. Two problems occur using the mentioned approach: 1. Due to various factors the climate conditions are changed and the precipitation intensity estimates need regular update; 2. As far as the extremes of the probability distribution are of particular importance for the practice, the methodology of the distribution fitting needs specific attention to those parts of the distribution. The aim of this paper is to make review of the existing methodologies for processing the intensive rainfalls and to refresh some of the statistical estimates for the studied areas. The methodologies used in Bulgaria for analyzing the intensive rainfalls and produce relevant statistical estimates: The method of the maximum intensity, used in the National Institute of Meteorology and Hydrology to process and decode the pluviometer's records, followed by distribution fitting for each precipitation duration period; As the above, but with separate modeling of probability distribution for the middle and high probability quantiles. Method is similar to the first one, but with a threshold of 0,36 mm/min of intensity; Another method proposed by the Russian hydrologist G. A. Aleksiev for regionalization of estimates over some territory, improved and adapted by S. Gerasimov for Bulgaria; Next method is considering only the intensive rainfalls (if any) during the day with the maximal annual daily precipitation total for a given year; Conclusions are drown on the relevance and adequacy of the applied methods.

Streamflow distribution maps for the Cannon River drainage basin, southeast Minnesota, and the St. Louis River drainage basin, northeast Minnesota

USGS Publications Warehouse

Smith, Erik A.; Sanocki, Chris A.; Lorenz, David L.; Jacobsen, Katrin E.

2017-12-27

Streamflow distribution maps for the Cannon River and St. Louis River drainage basins were developed by the U.S. Geological Survey, in cooperation with the Legislative-Citizen Commission on Minnesota Resources, to illustrate relative and cumulative streamflow distributions. The Cannon River was selected to provide baseline data to assess the effects of potential surficial sand mining, and the St. Louis River was selected to determine the effects of ongoing Mesabi Iron Range mining. Each drainage basin (Cannon, St. Louis) was subdivided into nested drainage basins: the Cannon River was subdivided into 152 nested drainage basins, and the St. Louis River was subdivided into 353 nested drainage basins. For each smaller drainage basin, the estimated volumes of groundwater discharge (as base flow) and surface runoff flowing into all surface-water features were displayed under the following conditions: (1) extreme low-flow conditions, comparable to an exceedance-probability quantile of 0.95; (2) low-flow conditions, comparable to an exceedance-probability quantile of 0.90; (3) a median condition, comparable to an exceedance-probability quantile of 0.50; and (4) a high-flow condition, comparable to an exceedance-probability quantile of 0.02.Streamflow distribution maps were developed using flow-duration curve exceedance-probability quantiles in conjunction with Soil-Water-Balance model outputs; both the flow-duration curve and Soil-Water-Balance models were built upon previously published U.S. Geological Survey reports. The selected streamflow distribution maps provide a proactive water management tool for State cooperators by illustrating flow rates during a range of hydraulic conditions. Furthermore, after the nested drainage basins are highlighted in terms of surface-water flows, the streamflows can be evaluated in the context of meeting specific ecological flows under different flow regimes and potentially assist with decisions regarding groundwater and surface-water appropriations. Presented streamflow distribution maps are foundational work intended to support the development of additional streamflow distribution maps that include statistical constraints on the selected flow conditions.

On the dependence on inclination of capture probability of short-period comets

NASA Astrophysics Data System (ADS)

Yabushita, S.; Tsujii, T.

1990-06-01

Calculation is made of probability of capture whereby a nearly parabolic comet with perihelion near the Jovian orbit comes to have a perihelion distance less than 2.5 AU and a period less than 200 yr. The probability is found to depend strongly on the inclination, in accordance with earlier results of Everhart and of Stagg and Bailey. It is large for orbits close to the ecliptic but decreases drastically for large inclinations. The overall probability of capture from randomly distributed orbits is 0.00044, which shows that either the presently observed short-period comets are not in a steady state or the source flux may be in the Uranus-Neptune zone.

Data Base for a National Mineral-Resource Assessment of Undiscovered Deposits of Gold, Silver, Copper, Lead, and Zinc in the Conterminous United States

USGS Publications Warehouse

Ludington, S.D.; Cox, D.P.; McCammon, R.B.

1996-01-01

For this assessment, the conterminous United States was divided into 12 regions Adirondack Mountains, Central and Southern Rocky Mountains, Colorado Plateau, East Central, Great Basin, Great Plains, Lake Superior, Northern Appalachians, Northern Rocky Mountains, Pacific Coast, Southern Appalachians, and Southern Basin and Range. The assessment, which was conducted by regional assessment teams of scientists from the USGS, was based on the concepts of permissive tracts and deposit models. Permissive tracts are discrete areas of the United States for which estimates of numbers of undiscovered deposits of a particular deposit type were made. A permissive tract is defined by its geographic boundaries such that the probability of deposits of the type delineated occurring outside the boundary is neglible. Deposit models, which are based on a compilation of worldwide literature and on observation, are sets of data in a convenient form that describe a group of deposits which have similar characteristics and that contain information on the common geologic attributes of the deposits and the environments in which they are found. Within each region, the assessment teams delineated permissive tracts for those deposit models that were judged to be appropriate and, when the amount of information warranted, estimated the number of undiscovered deposits. A total of 46 deposit models were used to assess 236 separate permissive tracts. Estimates of undiscovered deposits were limited to a depth of 1 km beneath the surface of the Earth. The estimates of the number of undiscovered deposits of gold, silver, copper, lead, and zinc were expressed in the form of a probability distribution. Commonly, the number of undiscovered deposits was estimated at the 90th, 50th, and 10th percentiles. A Monte Carlo simulation computer program was used to combine the probability distribution of the number of undiscovered deposits with the grade and tonnage data sets associated with each deposit model to obtain the probability distribution for undiscovered metal.

A smooth mixture of Tobits model for healthcare expenditure.

PubMed

Keane, Michael; Stavrunova, Olena

2011-09-01

This paper develops a smooth mixture of Tobits (SMTobit) model for healthcare expenditure. The model is a generalization of the smoothly mixing regressions framework of Geweke and Keane (J Econometrics 2007; 138: 257-290) to the case of a Tobit-type limited dependent variable. A Markov chain Monte Carlo algorithm with data augmentation is developed to obtain the posterior distribution of model parameters. The model is applied to the US Medicare Current Beneficiary Survey data on total medical expenditure. The results suggest that the model can capture the overall shape of the expenditure distribution very well, and also provide a good fit to a number of characteristics of the conditional (on covariates) distribution of expenditure, such as the conditional mean, variance and probability of extreme outcomes, as well as the 50th, 90th, and 95th, percentiles. We find that healthier individuals face an expenditure distribution with lower mean, variance and probability of extreme outcomes, compared with their counterparts in a worse state of health. Males have an expenditure distribution with higher mean, variance and probability of an extreme outcome, compared with their female counterparts. The results also suggest that heart and cardiovascular diseases affect the expenditure of males more than that of females. Copyright © 2011 John Wiley & Sons, Ltd.

Chance-Constrained Guidance With Non-Convex Constraints

NASA Technical Reports Server (NTRS)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

USGS Publications Warehouse

Asquith, William H.; Kiang, Julie E.; Cohn, Timothy A.

2017-07-17

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10–3 in scientific notation or for brevity 10–3). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10–3 to 10–6. Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

Emergence and stability of intermediate open vesicles in disk-to-vesicle transitions.

PubMed

Li, Jianfeng; Zhang, Hongdong; Qiu, Feng; Shi, An-Chang

2013-07-01

The transition between two basic structures, a disk and an enclosed vesicle, of a finite membrane is studied by examining the minimum energy path (MEP) connecting these two states. The MEP is constructed using the string method applied to continuum elastic membrane models. The results reveal that, besides the commonly observed disk and vesicle, open vesicles (bowl-shaped vesicles or vesicles with a pore) can become stable or metastable shapes. The emergence, stability, and probability distribution of these open vesicles are analyzed. It is demonstrated that open vesicles can be stabilized by higher-order elastic energies. The estimated probability distribution of the different structures is in good agreement with available experiments.

Electoral Susceptibility and Entropically Driven Interactions

NASA Astrophysics Data System (ADS)

Caravan, Bassir; Levine, Gregory

2013-03-01

In the United States electoral system the election is usually decided by the electoral votes cast by a small number of ``swing states'' where the two candidates historically have roughly equal probabilities of winning. The effective value of a swing state is determined not only by the number of its electoral votes but by the frequency of its appearance in the set of winning partitions of the electoral college. Since the electoral vote values of swing states are not identical, the presence or absence of a state in a winning partition is generally correlated with the frequency of appearance of other states and, hence, their effective values. We quantify the effective value of states by an electoral susceptibility, χj, the variation of the winning probability with the ``cost'' of changing the probability of winning state j. Associating entropy with the logarithm of the number of appearances of a state within the set of winning partitions, the entropy per state (in effect, the chemical potential) is not additive and the states may be said to ``interact.'' We study χj for a simple model with a Zipf's law type distribution of electoral votes. We show that the susceptibility for small states is largest in ``one-sided'' electoral contests and smallest in close contests. This research was supported by Department of Energy DE-FG02-08ER64623, Research Corporation CC6535 (GL) and HHMI Scholar Program (BC)

Observation of non-classical correlations in sequential measurements of photon polarization

NASA Astrophysics Data System (ADS)

Suzuki, Yutaro; Iinuma, Masataka; Hofmann, Holger F.

2016-10-01

A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.

A simulation of probabilistic wildfire risk components for the continental United States

Treesearch

Mark A. Finney; Charles W. McHugh; Isaac C. Grenfell; Karin L. Riley; Karen C. Short

2011-01-01

This simulation research was conducted in order to develop a large-fire risk assessment system for the contiguous land area of the United States. The modeling system was applied to each of 134 Fire Planning Units (FPUs) to estimate burn probabilities and fire size distributions. To obtain stable estimates of these quantities, fire ignition and growth was simulated for...

Theory of rotational transition in atom-diatom chemical reaction

NASA Astrophysics Data System (ADS)

Nakamura, Masato; Nakamura, Hiroki

1989-05-01

Rotational transition in atom-diatom chemical reaction is theoretically studied. A new approximate theory (which we call IOS-DW approximation) is proposed on the basis of the physical idea that rotational transition in reaction is induced by the following two different mechanisms: rotationally inelastic half collision in both initial and final arrangement channels, and coordinate transformation in the reaction zone. This theory gives a fairy compact expression for the state-to-state transition probability. Introducing the additional physically reasonable assumption that reaction (particle rearrangement) takes place in a spatially localized region, we have reduced this expression into a simpler analytical form which can explicitly give overall rotational state distribution in reaction. Numerical application was made to the H+H2 reaction and demonstrated its effectiveness for the simplicity. A further simplified most naive approximation, i.e., independent events approximation was also proposed and demonstrated to work well in the test calculation of H+H2. The overall rotational state distribution is expressed simply by a product sum of the transition probabilities for the three consecutive processes in reaction: inelastic transition in the initial half collision, transition due to particle rearrangement, and inelastic transition in the final half collision.

A moment-convergence method for stochastic analysis of biochemical reaction networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou, E-mail: mcszhtsh@mail.sysu.edu.cn

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in termsmore » of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.« less

On Probability Domains IV

NASA Astrophysics Data System (ADS)

Frič, Roman; Papčo, Martin

2017-12-01

Stressing a categorical approach, we continue our study of fuzzified domains of probability, in which classical random events are replaced by measurable fuzzy random events. In operational probability theory (S. Bugajski) classical random variables are replaced by statistical maps (generalized distribution maps induced by random variables) and in fuzzy probability theory (S. Gudder) the central role is played by observables (maps between probability domains). We show that to each of the two generalized probability theories there corresponds a suitable category and the two resulting categories are dually equivalent. Statistical maps and observables become morphisms. A statistical map can send a degenerated (pure) state to a non-degenerated one —a quantum phenomenon and, dually, an observable can map a crisp random event to a genuine fuzzy random event —a fuzzy phenomenon. The dual equivalence means that the operational probability theory and the fuzzy probability theory coincide and the resulting generalized probability theory has two dual aspects: quantum and fuzzy. We close with some notes on products and coproducts in the dual categories.

United States Geological Survey fire science: fire danger monitoring and forecasting

USGS Publications Warehouse

Eidenshink, Jeff C.; Howard, Stephen M.

2012-01-01

Each day, the U.S. Geological Survey produces 7-day forecasts for all Federal lands of the distributions of number of ignitions, number of fires above a given size, and conditional probabilities of fires growing larger than a specified size. The large fire probability map is an estimate of the likelihood that ignitions will become large fires. The large fire forecast map is a probability estimate of the number of fires on federal lands exceeding 100 acres in the forthcoming week. The ignition forecast map is a probability estimate of the number of fires on Federal land greater than 1 acre in the forthcoming week. The extreme event forecast is the probability estimate of the number of fires on Federal land that may exceed 5,000 acres in the forthcoming week.

State-space receptive fields of semicircular canal afferent neurons in the bullfrog

NASA Technical Reports Server (NTRS)

Paulin, M. G.; Hoffman, L. F.

2001-01-01

Receptive fields are commonly used to describe spatial characteristics of sensory neuron responses. They can be extended to characterize temporal or dynamical aspects by mapping neural responses in dynamical state spaces. The state-space receptive field of a neuron is the probability distribution of the dynamical state of the stimulus-generating system conditioned upon the occurrence of a spike. We have computed state-space receptive fields for semicircular canal afferent neurons in the bullfrog (Rana catesbeiana). We recorded spike times during broad-band Gaussian noise rotational velocity stimuli, computed the frequency distribution of head states at spike times, and normalized these to obtain conditional pdfs for the state. These state-space receptive fields quantify what the brain can deduce about the dynamical state of the head when a single spike arrives from the periphery. c2001 Elsevier Science B.V. All rights reserved.

Photodissociation of ethylbenzene and n-propylbenzene in a molecular beam

NASA Astrophysics Data System (ADS)

Huang, Cheng-Liang; Jiang, Jyh-Chiang; Lee, Yuan T.; Ni, Chi-Kung

2002-10-01

The photodissociation of jet-cooled ethylbenzene and n-propylbenzene at both 193 and 248 nm was studied using vacuum ultraviolet photoionization/multimass ion imaging techniques. The photofragment translational energy distributions from both the molecules obtained at 193 nm show that the probability of portioning energy to product translational energy decreases monotonically with increasing translational energy. They indicate that the dissociation occurs from the ground electronic state. However, the photofragment translational energy distributions from both molecules obtained at 248 nm contain a fast and a slow component. 75% of ethylbenzene and 80% of n-propylbenzene following the 248 nm photoexcitation dissociate from electronic excited state, resulting in the fast component. The remaining 25% of ethylbenzene and 20% of n-propylbenzene dissociate through the ground electronic state, giving rise to the slow component. A comparison with an ab initio calculation suggests that the dissociation from the first triplet state corresponds to the fast component in translational energy distribution.

Total coliform and E. coli in public water systems using undisinfected ground water in the United States.

PubMed

Messner, Michael J; Berger, Philip; Javier, Julie

2017-06-01

Public water systems (PWSs) in the United States generate total coliform (TC) and Escherichia coli (EC) monitoring data, as required by the Total Coliform Rule (TCR). We analyzed data generated in 2011 by approximately 38,000 small (serving fewer than 4101 individuals) undisinfected public water systems (PWSs). We used statistical modeling to characterize a distribution of TC detection probabilities for each of nine groupings of PWSs based on system type (community, non-transient non-community, and transient non-community) and population served (less than 101, 101-1000 and 1001-4100 people). We found that among PWS types sampled in 2011, on average, undisinfected transient PWSs test positive for TC 4.3% of the time as compared with 3% for undisinfected non-transient PWSs and 2.5% for undisinfected community PWSs. Within each type of PWS, the smaller systems have higher median TC detection than the larger systems. All TC-positive samples were assayed for EC. Among TC-positive samples from small undisinfected PWSs, EC is detected in about 5% of samples, regardless of PWS type or size. We evaluated the upper tail of the TC detection probability distributions and found that significant percentages of some system types have high TC detection probabilities. For example, assuming the systems providing data are nationally-representative, then 5.0% of the ∼50,000 small undisinfected transient PWSs in the U.S. have TC detection probabilities of 20% or more. Communities with such high TC detection probabilities may have elevated risk of acute gastrointestinal (AGI) illness - perhaps as great or greater than the attributable risk to drinking water (6-22%) calculated for 14 Wisconsin community PWSs with much lower TC detection probabilities (about 2.3%, Borchardt et al., 2012). Published by Elsevier GmbH.

Estimating transition probabilities in unmarked populations --entropy revisited

USGS Publications Warehouse

Cooch, E.G.; Link, W.A.

1999-01-01

The probability of surviving and moving between 'states' is of great interest to biologists. Robust estimation of these transitions using multiple observations of individually identifiable marked individuals has received considerable attention in recent years. However, in some situations, individuals are not identifiable (or have a very low recapture rate), although all individuals in a sample can be assigned to a particular state (e.g. breeding or non-breeding) without error. In such cases, only aggregate data (number of individuals in a given state at each occasion) are available. If the underlying matrix of transition probabilities does not vary through time and aggregate data are available for several time periods, then it is possible to estimate these parameters using least-squares methods. Even when such data are available, this assumption of stationarity will usually be deemed overly restrictive and, frequently, data will only be available for two time periods. In these cases, the problem reduces to estimating the most likely matrix (or matrices) leading to the observed frequency distribution of individuals in each state. An entropy maximization approach has been previously suggested. In this paper, we show that the entropy approach rests on a particular limiting assumption, and does not provide estimates of latent population parameters (the transition probabilities), but rather predictions of realized rates.

Evaluation of an Ensemble Dispersion Calculation.

NASA Astrophysics Data System (ADS)

Draxler, Roland R.

2003-02-01

A Lagrangian transport and dispersion model was modified to generate multiple simulations from a single meteorological dataset. Each member of the simulation was computed by assuming a ±1-gridpoint shift in the horizontal direction and a ±250-m shift in the vertical direction of the particle position, with respect to the meteorological data. The configuration resulted in 27 ensemble members. Each member was assumed to have an equal probability. The model was tested by creating an ensemble of daily average air concentrations for 3 months at 75 measurement locations over the eastern half of the United States during the Across North America Tracer Experiment (ANATEX). Two generic graphical displays were developed to summarize the ensemble prediction and the resulting concentration probabilities for a specific event: a probability-exceed plot and a concentration-probability plot. Although a cumulative distribution of the ensemble probabilities compared favorably with the measurement data, the resulting distribution was not uniform. This result was attributed to release height sensitivity. The trajectory ensemble approach accounts for about 41%-47% of the variance in the measurement data. This residual uncertainty is caused by other model and data errors that are not included in the ensemble design.

Design and development of a ceramic radial turbine for the AGT101

NASA Technical Reports Server (NTRS)

Finger, D. G.; Gupta, S. K.

1982-01-01

An acceptable and feasible ceramic turbine wheel design has been achieved, and the relevant temperature, stress, and success probability analyses are discussed. The design is described, the materials selection presented, and the engine cycle conditions analysis parameters shown. Measured MOR four-point strengths are indicated for room and elevated temperatures, and engine conditions are analyzed for various cycle states, materials, power states, turbine inlet temperatures, and speeds. An advanced gas turbine ceramic turbine rotor thermal and stress model is developed, and cumulative probability of survival is shown for first and third-year properties of SiC and Si3N4 rotors under different operating conditions, computed for both blade and hub regions. Temperature and stress distributions for steady-state and worst-case shutdown transients are depicted.

Security evaluation of the quantum key distribution system with two-mode squeezed states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osaki, M.; Ban, M.

2003-08-01

The quantum key distribution (QKD) system with two-mode squeezed states has been demonstrated by Pereira et al. [Phys. Rev. A 62, 042311 (2000)]. They evaluate the security of the system based on the signal to noise ratio attained by a homodyne detector. In this paper, we discuss its security based on the error probability individually attacked by eavesdropper with the unambiguous or the error optimum detection. The influence of the energy loss at transmission channels is also taken into account. It will be shown that the QKD system is secure under these conditions.

Estimating rate constants from single ion channel currents when the initial distribution is known.

PubMed

The, Yu-Kai; Fernandez, Jacqueline; Popa, M Oana; Lerche, Holger; Timmer, Jens

2005-06-01

Single ion channel currents can be analysed by hidden or aggregated Markov models. A classical result from Fredkin et al. (Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, vol I, pp 269-289, 1985) states that the maximum number of identifiable parameters is bounded by 2n(o)n(c), where n(o) and n(c) denote the number of open and closed states, respectively. We show that this bound can be overcome when the probabilities of the initial distribution are known and the data consist of several sweeps.

A hydroclimatological approach to predicting regional landslide probability using Landlab

NASA Astrophysics Data System (ADS)

Strauch, Ronda; Istanbulluoglu, Erkan; Nudurupati, Sai Siddhartha; Bandaragoda, Christina; Gasparini, Nicole M.; Tucker, Gregory E.

2018-02-01

We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m), and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.

Delay-distribution-dependent H∞ state estimation for delayed neural networks with (x,v)-dependent noises and fading channels.

PubMed

Sheng, Li; Wang, Zidong; Tian, Engang; Alsaadi, Fuad E

2016-12-01

This paper deals with the H ∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H ∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

Fox, Colin; Morrison, Malcolm E. K.; Norton, Richard A.; Molteno, Timothy C. A.

2018-01-01

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Improved techniques for outgoing wave variational principle calculations of converged state-to-state transition probabilities for chemical reactions

NASA Technical Reports Server (NTRS)

Mielke, Steven L.; Truhlar, Donald G.; Schwenke, David W.

1991-01-01

Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.

Breakdown of the classical description of a local system.

PubMed

Kot, Eran; Grønbech-Jensen, Niels; Nielsen, Bo M; Neergaard-Nielsen, Jonas S; Polzik, Eugene S; Sørensen, Anders S

2012-06-08

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A 83, 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Applications of the first digit law to measure correlations.

PubMed

Gramm, R; Yost, J; Su, Q; Grobe, R

2017-04-01

The quasiempirical Benford law predicts that the distribution of the first significant digit of random numbers obtained from mixed probability distributions is surprisingly meaningful and reveals some universal behavior. We generalize this finding to examine the joint first-digit probability of a pair of two random numbers and show that undetectable correlations by means of the usual covariance-based measure can be identified in the statistics of the corresponding first digits. We illustrate this new measure by analyzing the correlations and anticorrelations of the positions of two interacting particles in their quantum mechanical ground state. This suggests that by using this measure, the presence or absence of correlations can be determined even if only the first digit of noisy experimental data can be measured accurately.

Modeling of Abrasion and Crushing of Unbound Granular Materials During Compaction

NASA Astrophysics Data System (ADS)

Ocampo, Manuel S.; Caicedo, Bernardo

2009-06-01

Unbound compacted granular materials are commonly used in engineering structures as layers in road pavements, railroad beds, highway embankments, and foundations. These structures are generally subjected to dynamic loading by construction operations, traffic and wheel loads. These repeated or cyclic loads cause abrasion and crushing of the granular materials. Abrasion changes a particle's shape, and crushing divides the particle into a mixture of many small particles of varying sizes. Particle breakage is important because the mechanical and hydraulic properties of these materials depend upon their grain size distribution. Therefore, it is important to evaluate the evolution of the grain size distribution of these materials. In this paper an analytical model for unbound granular materials is proposed in order to evaluate particle crushing of gravels and soils subjected to cyclic loads. The model is based on a Markov chain which describes the development of grading changes in the material as a function of stress levels. In the model proposed, each particle size is a state in the system, and the evolution of the material is the movement of particles from one state to another in n steps. Each step is a load cycle, and movement between states is possible with a transition probability. The crushing of particles depends on the mechanical properties of each grain and the packing density of the granular material. The transition probability was calculated using both the survival probability defined by Weibull and the compressible packing model developed by De Larrard. Material mechanical properties are considered using the Weibull probability theory. The size and shape of the grains, as well as the method of processing the packing density are considered using De Larrard's model. Results of the proposed analytical model show a good agreement with the experimental tests carried out using the gyratory compaction test.

Earth Observing System Covariance Realism

NASA Technical Reports Server (NTRS)

Zaidi, Waqar H.; Hejduk, Matthew D.

2016-01-01

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Future changes in South American biomass distributions, biome distributions and plant trait spectra is dependent on applied atmospheric forcings.

NASA Astrophysics Data System (ADS)

Langan, Liam; Scheiter, Simon; Higgins, Steven

2017-04-01

It remains poorly understood why the position of the forest-savanna biome boundary, in a domain defined by precipitation and temperature, differs in South America, Africa and Australia. Process based Dynamic Global Vegetation Models (DGVMs) are a valuable tool to investigate the determinants of vegetation distributions, however, many DGVMs fail to predict the spatial distribution or indeed presence of the South American savanna biome. Evidence suggests fire plays a significant role in mediating forest-savanna biome boundaries, however, fire alone appear to be insufficient to predict these boundaries in South America. We hypothesize that interactions between precipitation, constraints on tree rooting depth and fire, affect the probability of savanna occurrence and the position of the savanna-forest boundary. We tested our hypotheses at tropical forest and savanna sites in Brazil and Venezuela using a novel DGVM, aDGVM2, which allows plant trait spectra, constrained by trade-offs between traits, to evolve in response to abiotic and biotic conditions. Plant hydraulics is represented by the cohesion-tension theory, this allowed us to explore how soil and plant hydraulics control biome distributions and plant traits. The resulting community trait distributions are emergent properties of model dynamics. We showed that across much of South America the biome state is not determined by climate alone. Interactions between tree rooting depth, fire and precipitation affected the probability of observing a given biome state and the emergent traits of plant communities. Simulations where plant rooting depth varied in space provided the best match to satellite derived biomass estimates and generated biome distributions that reproduced contemporary biome maps well. Future projections showed that biomass distributions, biome distributions and plant trait spectra will change, however, the magnitude of these changes are highly dependent on the applied atmospheric forcings.

Quenching of highly vibrationally excited pyrimidine by collisions with CO2

NASA Astrophysics Data System (ADS)

Johnson, Jeremy A.; Duffin, Andrew M.; Hom, Brian J.; Jackson, Karl E.; Sevy, Eric T.

2008-02-01

Relaxation of highly vibrationally excited pyrimidine (C4N2H4) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot pyrimidine (E'=40635cm-1) was prepared by 248-nm excimer laser excitation, followed by rapid radiationless relaxation to the ground electronic state. The nascent rotational population distribution (J=58-80) of the 0000 ground state of CO2 resulting from collisions with hot pyrimidine was probed at short times following the excimer laser pulse. Doppler spectroscopy was used to measure the CO2 recoil velocity distribution for J =58-80 of the 0000 state. Rate constants and probabilities for collisions populating these CO2 rotational states were determined. The measured energy transfer probabilities, indexed by final bath state, were resorted as a function of ΔE to create the energy transfer distribution function, P(E,E'), from E'-E˜1300-7000cm-1. P(E,E') is fitted to a single exponential and a biexponential function to determine the average energy transferred in a single collision between pyrimidine and CO2 and parameters that can be compared to previously studied systems using this technique, pyrazine/CO2, C6F6/CO2, and methylpyrazine/CO2. P(E,E') parameters for these four systems are also compared to various molecular properties of the donor molecules. Finally, P(E,E') is analyzed in the context of two models, one which suggests that the shape of P(E,E') is primarily determined by the low-frequency out-of-plane donor vibrational modes and one which suggests that the shape of P(E,E') can be determined by how the donor molecule final density of states changes with ΔE.

The classification of flaring states of blazars

NASA Astrophysics Data System (ADS)

Resconi, E.; Franco, D.; Gross, A.; Costamante, L.; Flaccomio, E.

2009-08-01

Aims: The time evolution of the electromagnetic emission from blazars, in particular high-frequency peaked sources (HBLs), displays irregular activity that has not yet been understood. In this work we report a methodology capable of characterizing the time behavior of these variable objects. Methods: The maximum likelihood blocks (MLBs) is a model-independent estimator that subdivides the light curve into time blocks, whose length and amplitude are compatible with states of constant emission rate of the observed source. The MLBs yield the statistical significance in the rate variations and strongly suppresses the noise fluctuations in the light curves. We applied the MLBs for the first time on the long term X-ray light curves (RXTE/ASM) of Mkn 421, Mkn 501, 1ES 1959+650, and 1ES 2155-304, more than 10 years of observational data (1996-2007). Using the MLBs interpretation of RXTE/ASM data, the integrated time flux distribution is determined for each single source considered. We identify in these distributions the characteristic level, as well as the flaring states of the blazars. Results: All the distributions show a significant component at negative flux values, most probably caused by an uncertainty in the background subtraction and by intrinsic fluctuations of RXTE/ASM. This effect concerns in particular short time observations. To quantify the probability that the intrinsic fluctuations give rise to a false identification of a flare, we study a population of very faint sources and their integrated time-flux distribution. We determine duty cycle or fraction of time a source spent in the flaring state of the source Mkn 421, Mkn 501, 1ES 1959+650 and 1ES 2155-304. Moreover, we study the random coincidences between flares and generic sporadic events such as high-energy neutrinos or flares in other wavelengths.

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

NASA Astrophysics Data System (ADS)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

NASA Astrophysics Data System (ADS)

Chen, Yen-Luan; Chang, Chin-Chih; Sheu, Dwan-Fang

2016-04-01

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Models of multidimensional discrete distribution of probabilities of random variables in information systems

NASA Astrophysics Data System (ADS)

Gromov, Yu Yu; Minin, Yu V.; Ivanova, O. G.; Morozova, O. N.

2018-03-01

Multidimensional discrete distributions of probabilities of independent random values were received. Their one-dimensional distribution is widely used in probability theory. Producing functions of those multidimensional distributions were also received.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

PubMed

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

The Generalized Quantum Episodic Memory Model.

PubMed

Trueblood, Jennifer S; Hemmer, Pernille

2017-11-01

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory. Copyright © 2016 Cognitive Science Society, Inc.

REGRESSION ON MEDIANS OF PROBABILITY DISTRIBUTIONS

EPA Science Inventory

The median is a fundamental parameter in the area of lifetime and survival statistics. n toxicodynamics the LD50, lethal dose that results in 50% mortality, is frequently used. he median is also used to describe the incidence of cancer and other disease states. Factors such as nu...

ACARA - AVAILABILITY, COST AND RESOURCE ALLOCATION

NASA Technical Reports Server (NTRS)

Viterna, L. A.

1994-01-01

ACARA is a program for analyzing availability, lifecycle cost, and resource scheduling. It uses a statistical Monte Carlo method to simulate a system's capacity states as well as component failure and repair. Component failures are modelled using a combination of exponential and Weibull probability distributions. ACARA schedules component replacement to achieve optimum system performance. The scheduling will comply with any constraints on component production, resupply vehicle capacity, on-site spares, or crew manpower and equipment. ACARA is capable of many types of analyses and trade studies because of its integrated approach. It characterizes the system performance in terms of both state availability and equivalent availability (a weighted average of state availability). It can determine the probability of exceeding a capacity state to assess reliability and loss of load probability. It can also evaluate the effect of resource constraints on system availability and lifecycle cost. ACARA interprets the results of a simulation and displays tables and charts for: (1) performance, i.e., availability and reliability of capacity states, (2) frequency of failure and repair, (3) lifecycle cost, including hardware, transportation, and maintenance, and (4) usage of available resources, including mass, volume, and maintenance man-hours. ACARA incorporates a user-friendly, menu-driven interface with full screen data entry. It provides a file management system to store and retrieve input and output datasets for system simulation scenarios. ACARA is written in APL2 using the APL2 interpreter for IBM PC compatible systems running MS-DOS. Hardware requirements for the APL2 system include 640K of RAM, 2Mb of extended memory, and an 80386 or 80486 processor with an 80x87 math co-processor. A dot matrix printer is required if the user wishes to print a graph from a results table. A sample MS-DOS executable is provided on the distribution medium. The executable contains licensed material from the APL2 for the IBM PC product which is program property of IBM; Copyright IBM Corporation 1988 - All rights reserved. It is distributed with IBM's permission. The standard distribution medium for this program is a set of three 5.25 inch 360K MS-DOS format diskettes. The contents of the diskettes are compressed using the PKWARE archiving tools. The utility to unarchive the files, PKUNZIP.EXE, is included. ACARA was developed in 1992.

Hydrodynamic Flow Fluctuations in √sNN = 5:02 TeV PbPbCollisions

NASA Astrophysics Data System (ADS)

Castle, James R.

The collective, anisotropic expansion of the medium created in ultrarelativistic heavy-ion collisions, known as flow, is characterized through a Fourier expansion of the final-state azimuthal particle density. In the Fourier expansion, flow harmonic coefficients vn correspond to shape components in the final-state particle density, which are a consequence of similar spatial anisotropies in the initial-state transverse energy density of a collision. Flow harmonic fluctuations are studied for PbPb collisions at √sNN = 5.02 TeV using the CMS detector at the CERN LHC. Flow harmonic probability distributions p( vn) are obtained using particles with 0.3 < pT < 3.0 GeV/c and ∥eta∥ < 1.0 by removing finite-multiplicity resolution effects from the observed azimuthal particle density through an unfolding procedure. Cumulant elliptic flow harmonics (n = 2) are determined from the moments of the unfolded p(v2) distributions and used to construct observables in 5% wide centrality bins up to 60% that relate to the initial-state spatial anisotropy. Hydrodynamic models predict that fluctuations in the initial-state transverse energy density will lead to a non-Gaussian component in the elliptic flow probability distributions that manifests as a negative skewness. A statistically significant negative skewness is observed for all centrality bins as evidenced by a splitting between the higher-order cumulant elliptic flow harmonics. The unfolded p (v2) distributions are transformed assuming a linear relationship between the initial-state spatial anisotropy and final-state flow and are fitted with elliptic power law and Bessel Gaussian parametrizations to infer information on the nature of initial-state fluctuations. The elliptic power law parametrization is found to provide a more accurate description of the fluctuations than the Bessel-Gaussian parametrization. In addition, the event-shape engineering technique, where events are further divided into classes based on an observed ellipticity, is used to study fluctuation-driven differences in the initial-state spatial anisotropy for a given collision centrality that would otherwise be destroyed by event-averaging techniques. Correlations between the first and second moments of p( vn) distributions and event ellipticity are measured for harmonic orders n = 2 - 4 by coupling event-shape engineering to the unfolding technique.

Monitoring multiple species: Estimating state variables and exploring the efficacy of a monitoring program

USGS Publications Warehouse

Mattfeldt, S.D.; Bailey, L.L.; Grant, E.H.C.

2009-01-01

Monitoring programs have the potential to identify population declines and differentiate among the possible cause(s) of these declines. Recent criticisms regarding the design of monitoring programs have highlighted a failure to clearly state objectives and to address detectability and spatial sampling issues. Here, we incorporate these criticisms to design an efficient monitoring program whose goals are to determine environmental factors which influence the current distribution and measure change in distributions over time for a suite of amphibians. In designing the study we (1) specified a priori factors that may relate to occupancy, extinction, and colonization probabilities and (2) used the data collected (incorporating detectability) to address our scientific questions and adjust our sampling protocols. Our results highlight the role of wetland hydroperiod and other local covariates in the probability of amphibian occupancy. There was a change in overall occupancy probabilities for most species over the first three years of monitoring. Most colonization and extinction estimates were constant over time (years) and space (among wetlands), with one notable exception: local extinction probabilities for Rana clamitans were lower for wetlands with longer hydroperiods. We used information from the target system to generate scenarios of population change and gauge the ability of the current sampling to meet monitoring goals. Our results highlight the limitations of the current sampling design, emphasizing the need for long-term efforts, with periodic re-evaluation of the program in a framework that can inform management decisions.

Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

PubMed

Semenov, Yuri S; Novozhilov, Artem S

2015-08-01

We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. Copyright © 2015. Published by Elsevier Inc.

Geospatial tools effectively estimate nonexceedance probabilities of daily streamflow at ungauged and intermittently gauged locations in Ohio

USGS Publications Warehouse

Farmer, William H.; Koltun, Greg

2017-01-01

Study regionThe state of Ohio in the United States, a humid, continental climate.Study focusThe estimation of nonexceedance probabilities of daily streamflows as an alternative means of establishing the relative magnitudes of streamflows associated with hydrologic and water-quality observations.New hydrological insights for the regionSeveral methods for estimating nonexceedance probabilities of daily mean streamflows are explored, including single-index methodologies (nearest-neighboring index) and geospatial tools (kriging and topological kriging). These methods were evaluated by conducting leave-one-out cross-validations based on analyses of nearly 7 years of daily streamflow data from 79 unregulated streamgages in Ohio and neighboring states. The pooled, ordinary kriging model, with a median Nash–Sutcliffe performance of 0.87, was superior to the single-site index methods, though there was some bias in the tails of the probability distribution. Incorporating network structure through topological kriging did not improve performance. The pooled, ordinary kriging model was applied to 118 locations without systematic streamgaging across Ohio where instantaneous streamflow measurements had been made concurrent with water-quality sampling on at least 3 separate days. Spearman rank correlations between estimated nonexceedance probabilities and measured streamflows were high, with a median value of 0.76. In consideration of application, the degree of regulation in a set of sample sites helped to specify the streamgages required to implement kriging approaches successfully.

Bound entangled states with a private key and their classical counterpart.

PubMed

Ozols, Maris; Smith, Graeme; Smolin, John A

2014-03-21

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question--they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with a private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract a key from them.

Cost of Crashes Related to Road Conditions, United States, 2006

PubMed Central

Zaloshnja, Eduard; Miller, Ted R.

2009-01-01

This is the first study to estimate the cost of crashes related to road conditions in the U.S. To model the probability that road conditions contributed to the involvement of a vehicle in the crash, we used 2000–03 Large Truck Crash Causation Study (LTCCS) data, the only dataset that provides detailed information whether road conditions contributed to crash occurrence. We applied the logistic regression results to a costed national crash dataset in order to calculate the probability that road conditions contributed to the involvement of a vehicle in each crash. In crashes where someone was moderately to seriously injured (AIS-2-6) in a vehicle that harmfully impacted a large tree or medium or large non-breakaway pole, or if the first harmful event was collision with a bridge, we changed the calculated probability of being road-related to 1. We used the state distribution of costs of fatal crashes where road conditions contributed to crash occurrence or severity to estimate the respective state distribution of non-fatal crash costs. The estimated comprehensive cost of traffic crashes where road conditions contributed to crash occurrence or severity was $217.5 billion in 2006. This represented 43.6% of the total comprehensive crash cost. The large share of crash costs related to road design and conditions underlines the importance of these factors in highway safety. Road conditions are largely controllable. Road maintenance and upgrading can prevent crashes and reduce injury severity. PMID:20184840

A performability solution method for degradable nonrepairable systems

NASA Technical Reports Server (NTRS)

Furchtgott, D. G.; Meyer, J. F.

1984-01-01

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

State-space modeling to support management of brucellosis in the Yellowstone bison population

USGS Publications Warehouse

Hobbs, N. Thompson; Geremia, Chris; Treanor, John; Wallen, Rick; White, P.J.; Hooten, Mevin B.; Rhyan, Jack C.

2015-01-01

The bison (Bison bison) of the Yellowstone ecosystem, USA, exemplify the difficulty of conserving large mammals that migrate across the boundaries of conservation areas. Bison are infected with brucellosis (Brucella abortus) and their seasonal movements can expose livestock to infection. Yellowstone National Park has embarked on a program of adaptive management of bison, which requires a model that assimilates data to support management decisions. We constructed a Bayesian state-space model to reveal the influence of brucellosis on the Yellowstone bison population. A frequency-dependent model of brucellosis transmission was superior to a density-dependent model in predicting out-of-sample observations of horizontal transmission probability. A mixture model including both transmission mechanisms converged on frequency dependence. Conditional on the frequency-dependent model, brucellosis median transmission rate was 1.87 yr−1. The median of the posterior distribution of the basic reproductive ratio (R0) was 1.75. Seroprevalence of adult females varied around 60% over two decades, but only 9.6 of 100 adult females were infectious. Brucellosis depressed recruitment; estimated population growth rate λ averaged 1.07 for an infected population and 1.11 for a healthy population. We used five-year forecasting to evaluate the ability of different actions to meet management goals relative to no action. Annually removing 200 seropositive female bison increased by 30-fold the probability of reducing seroprevalence below 40% and increased by a factor of 120 the probability of achieving a 50% reduction in transmission probability relative to no action. Annually vaccinating 200 seronegative animals increased the likelihood of a 50% reduction in transmission probability by fivefold over no action. However, including uncertainty in the ability to implement management by representing stochastic variation in the number of accessible bison dramatically reduced the probability of achieving goals using interventions relative to no action. Because the width of the posterior predictive distributions of future population states expands rapidly with increases in the forecast horizon, managers must accept high levels of uncertainty. These findings emphasize the necessity of iterative, adaptive management with relatively short-term commitment to action and frequent reevaluation in response to new data and model forecasts. We believe our approach has broad applications.

Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem

NASA Astrophysics Data System (ADS)

Busch, P.

2003-09-01

A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple proof of the result, analogous to Gleason’s theorem, that any quantum state is given by a density operator. As a corollary we obtain a vonNeumann type argument against noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.

Mechanisms of DNA disentangling by type II topoisomerases. Comment on "Disentangling DNA molecules" by Alexander Vologodskii

NASA Astrophysics Data System (ADS)

Yan, Jie

2016-09-01

In this article [1] Dr. Vologodskii presents a comprehensive discussion on the mechanisms by which the type II topoisomerases unknot/disentangle DNA molecules. It is motivated by a mysterious capability of the nanometer-size enzymes to keep the steady-state probability of DNA entanglement/knot almost two orders of magnitude below that expected from thermal equilibrium [2-5]. In spite of obvious functional advantages of the enzymes, it raises a question regarding how such high efficiency could be achieved. The off-equilibrium steady state distribution of DNA topology is powered by ATP consumption. However, it remains unclear how this energy is utilized to bias the distribution toward disentangled/unknotted topological states of DNA.

Crowding Effects in Vehicular Traffic

PubMed Central

Combinido, Jay Samuel L.; Lim, May T.

2012-01-01

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems. PMID:23139762

Coherent state amplification using frequency conversion and a single photon source

NASA Astrophysics Data System (ADS)

Kasture, Sachin

2017-11-01

Quantum state discrimination lies at the heart of quantum communication and quantum cryptography protocols. Quantum Key Distribution (QKD) using coherent states and homodyne detection has been shown to be a feasible method for quantum communication over long distances. However, this method is still limited because of optical losses. Noiseless coherent state amplification has been proposed as a way to overcome this. Photon addition using stimulated Spontaneous Parametric Down-conversion followed by photon subtraction has been used as a way to implement amplification. However, this process occurs with very low probability which makes it very difficult to implement cascaded stages of amplification due to dark count probability in the single photon detectors used to herald the addition and subtraction of single photons. We discuss a scheme using the χ (2) and χ (3) optical non-linearity and frequency conversion (sum and difference frequency generation) along with a single photon source to implement photon addition. Unlike the photon addition scheme using SPDC, this scheme allows us to tune the success probability at the cost of reduced amplification. The photon statistics of the converted field can be controlled using the power of the pump field and the interaction time.

Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density.

PubMed

Tygert, Mark

2010-09-21

We discuss several tests for determining whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).

Interpolating Non-Parametric Distributions of Hourly Rainfall Intensities Using Random Mixing

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András; Hörning, Sebastian

2015-04-01

The correct spatial interpolation of hourly rainfall intensity distributions is of great importance for stochastical rainfall models. Poorly interpolated distributions may lead to over- or underestimation of rainfall and consequently to wrong estimates of following applications, like hydrological or hydraulic models. By analyzing the spatial relation of empirical rainfall distribution functions, a persistent order of the quantile values over a wide range of non-exceedance probabilities is observed. As the order remains similar, the interpolation weights of quantile values for one certain non-exceedance probability can be applied to the other probabilities. This assumption enables the use of kernel smoothed distribution functions for interpolation purposes. Comparing the order of hourly quantile values over different gauges with the order of their daily quantile values for equal probabilities, results in high correlations. The hourly quantile values also show high correlations with elevation. The incorporation of these two covariates into the interpolation is therefore tested. As only positive interpolation weights for the quantile values assure a monotonically increasing distribution function, the use of geostatistical methods like kriging is problematic. Employing kriging with external drift to incorporate secondary information is not applicable. Nonetheless, it would be fruitful to make use of covariates. To overcome this shortcoming, a new random mixing approach of spatial random fields is applied. Within the mixing process hourly quantile values are considered as equality constraints and correlations with elevation values are included as relationship constraints. To profit from the dependence of daily quantile values, distribution functions of daily gauges are used to set up lower equal and greater equal constraints at their locations. In this way the denser daily gauge network can be included in the interpolation of the hourly distribution functions. The applicability of this new interpolation procedure will be shown for around 250 hourly rainfall gauges in the German federal state of Baden-Württemberg. The performance of the random mixing technique within the interpolation is compared to applicable kriging methods. Additionally, the interpolation of kernel smoothed distribution functions is compared with the interpolation of fitted parametric distributions.

The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

NASA Astrophysics Data System (ADS)

Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš

2018-04-01

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

Polarization effects on quantum levels in InN/GaN quantum wells.

PubMed

Lin, Wei; Li, Shuping; Kang, Junyong

2009-12-02

Polarization effects on quantum states in InN/GaN quantum wells have been investigated by means of ab initio calculation and spectroscopic ellipsometry. Through the position-dependent partial densities of states, our results show that the polarization modified by the strain with different well thickness leads to an asymmetry band bending of the quantum well. The quantum levels are identified via the band structures and their square wave function distributions are analyzed by the partial charge densities. Further theoretical and experimental comparison of the imaginary part of the dielectric function show that the overall transition probability increases under larger polarization fields, which can be attributable to the fact that the excited quantum states of 2h have a greater overlap with 1e states and enhance other hole quantum states in the well by a hybridization. These results would provide a new approach to improve the transition probability and light emission by enhancing the polarization fields in a proper way.

Multi-photon self-error-correction hyperentanglement distribution over arbitrary collective-noise channels

NASA Astrophysics Data System (ADS)

Gao, Cheng-Yan; Wang, Guan-Yu; Zhang, Hao; Deng, Fu-Guo

2017-01-01

We present a self-error-correction spatial-polarization hyperentanglement distribution scheme for N-photon systems in a hyperentangled Greenberger-Horne-Zeilinger state over arbitrary collective-noise channels. In our scheme, the errors of spatial entanglement can be first averted by encoding the spatial-polarization hyperentanglement into the time-bin entanglement with identical polarization and defined spatial modes before it is transmitted over the fiber channels. After transmission over the noisy channels, the polarization errors introduced by the depolarizing noise can be corrected resorting to the time-bin entanglement. Finally, the parties in quantum communication can in principle share maximally hyperentangled states with a success probability of 100%.

Can we expect to predict climate if we cannot shadow weather?

NASA Astrophysics Data System (ADS)

Smith, Leonard

2010-05-01

What limits our ability to predict (or project) useful statistics of future climate? And how might we quantify those limits? In the early 1960s, Ed Lorenz illustrated one constraint on point forecasts of the weather (chaos) while noting another (model imperfections). In the mid-sixties he went on to discuss climate prediction, noting that chaos, per se, need not limit accurate forecasts of averages and the distributions that define climate. In short, chaos might place draconian limits on what we can say about a particular summer day in 2010 (or 2040), but it need not limit our ability to make accurate and informative statements about the weather over this summer as a whole, or climate distributions of the 2040's. If not chaos, what limits our ability to produce decision relevant probability distribution functions (PDFs)? Is this just a question of technology (raw computer power) and uncertain boundary conditions (emission scenarios)? Arguably, current model simulations of the Earth's climate are limited by model inadequacy: not that the initial or boundary conditions are unknown but that state-of-the-art models would not yield decision-relevant probability distributions even if they were known. Or to place this statement in an empirically falsifiable format: that in 2100 when the boundary conditions are known and computer power is (hopefully) sufficient to allow exhaustive exploration of today's state-of-the-art models: we will find today's models do not admit a trajectory consistent with our knowledge of the state of the earth in 2009 which would prove of decision support relevance for, say, 25 km, hourly resolution. In short: today's models cannot shadow the weather of this century even after the fact. Restating this conjecture in a more positive frame: a 2100 historian of science will be able to determine the highest space and time scales on which 2009 models could have (i) produced trajectories plausibly consistent with the (by then) observed twenty-first century and (ii) produced probability distributions useful as such for decision support. As it will be some time until such conjectures can be refuted, how might we best advise decision makers of the detail (specifically, space and time resolution of a quantity of interest as a function of lead-time) that it is rational to interpret model-based PDFs as decision-relevant probability distributions? Given the nonlinearities already incorporated in our models, how far into the future can one expect a simulation to get the temperature "right" given the simulation has precipitation badly "wrong"? When can biases in local temperature which melt model-ice no longer be dismissed, and neglected by presenting model-anomalies? At what lead times will feedbacks due to model inadequacies cause the 2007 model simulations to drift away from what today's basic science (and 2100 computer power) would suggest? How might one justify quantitative claims regarding "extreme events" (or NUMB weather)? Models are unlikely to forecast things they cannot shadow, or at least track. There is no constraint on rational scientists to take model distributions as their subjective probabilities, unless they believe the model is empirically adequate. How then are we to use today's simulations to inform today's decisions? Two approaches are considered. The first augments the model-based PDF with an explicit subjective-probability of a "Big Surprise". The second is to look not for a PDF but, following Solvency II, consider the risk from any event that cannot be ruled out at, say, the one in 200 level. The fact that neither approach provides the simplicity and apparent confidence of interpreting model-based PDFs as if they were objective probabilities does not contradict the claim that either might lead to better decision-making.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Update rules and interevent time distributions: slow ordering versus no ordering in the voter model.

PubMed

Fernández-Gracia, J; Eguíluz, V M; San Miguel, M

2011-07-01

We introduce a general methodology of update rules accounting for arbitrary interevent time (IET) distributions in simulations of interacting agents. We consider in particular update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully connected, random, and scale-free networks with an activation probability inversely proportional to the time since the last action, where an action can be an update attempt (an exogenous update) or a change of state (an endogenous update). We find that in the thermodynamic limit, at variance with standard updates and the exogenous update, the system orders slowly for the endogenous update. The approach to the absorbing state is characterized by a power-law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined. The IET distributions resulting from both update schemes show power-law tails.

A maximum entropy thermodynamics of small systems.

PubMed

Dixit, Purushottam D

2013-05-14

We present a maximum entropy approach to analyze the state space of a small system in contact with a large bath, e.g., a solvated macromolecular system. For the solute, the fluctuations around the mean values of observables are not negligible and the probability distribution P(r) of the state space depends on the intricate details of the interaction of the solute with the solvent. Here, we employ a superstatistical approach: P(r) is expressed as a marginal distribution summed over the variation in β, the inverse temperature of the solute. The joint distribution P(β, r) is estimated by maximizing its entropy. We also calculate the first order system-size corrections to the canonical ensemble description of the state space. We test the development on a simple harmonic oscillator interacting with two baths with very different chemical identities, viz., (a) Lennard-Jones particles and (b) water molecules. In both cases, our method captures the state space of the oscillator sufficiently well. Future directions and connections with traditional statistical mechanics are discussed.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

NASA Astrophysics Data System (ADS)

Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin

2018-01-01

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn; Ide, Yusuke

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coinmore » and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.« less

Evolution of ion emission yield of alloys with the nature of the solute. 2: Interpretation

NASA Technical Reports Server (NTRS)

Blaise, G.; Slodzian, G.

1977-01-01

Solid solutions of transition elements in copper, nickel, cobalt, iron, and aluminum matrices were analyzed by observing secondary ion emissions under bombardment with 6.2-keV argon ions. Enchancement of the production of solute-element ions was observed. An ion emission model is proposed according to which the ion yield is governed by the probability of an atom leaving the metal in a preionized state. The energy distribution of the valence electrons of the solute atoms is the bases of the probability calculation.

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

Statistical analysis of general aviation VG-VGH data

NASA Technical Reports Server (NTRS)

Clay, L. E.; Dickey, R. L.; Moran, M. S.; Payauys, K. W.; Severyn, T. P.

1974-01-01

To represent the loads spectra of general aviation aircraft operating in the Continental United States, VG and VGH data collected since 1963 in eight operational categories were processed and analyzed. Adequacy of data sample and current operational categories, and parameter distributions required for valid data extrapolation were studied along with envelopes of equal probability of exceeding the normal load factor (n sub z) versus airspeed for gust and maneuver loads and the probability of exceeding current design maneuver, gust, and landing impact n sub z limits. The significant findings are included.

ENSO Dynamics and Trends, AN Alternate View

NASA Astrophysics Data System (ADS)

Rojo Hernandez, J. D.; Lall, U.; Mesa, O. J.

2017-12-01

El Niño - Southern Oscillation (ENSO) is the most important inter-annual climate fluctuation on a planetary level with great effects on the hydrological cycle, agriculture, ecosystems, health and society. This work demonstrates the use of the Non-Homogeneus hidden Markov Models (NHMM) to characterize ENSO using a set of discrete states with variable transition probabilities matrix using the data of sea surface temperature anomalies (SSTA) of the Kaplan Extended SST v2 between 120E -90W, 15N-15S from Jan-1856 to Dec-2016. ENSO spatial patterns, their temporal distribution, the transition probabilities between patterns and their temporal evolution are the main results of the NHHMM applied to ENSO. The five "hidden" states found appear to represent the different "Flavors" described in the literature: the Canonical El Niño, Central El Niño, a Neutral state, Central La Niña and the Canonical Niña. Using the whole record length of the SSTA it was possible to identify trends in the dynamic system, with a decrease in the probability of occurrence of the cold events and a significant increase of the warm events, in particular of Central El Niño events whose probability of occurrence has increased Dramatically since 1960 coupled with increases in global temperature.

Noninformative prior in the quantum statistical model of pure states

NASA Astrophysics Data System (ADS)

Tanaka, Fuyuhiko

2012-06-01

In the present paper, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure-states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of a pure-states model. Theoretically, it gives one of the ways that we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum-state tomography with a small sample.

Charge-state distribution of Li ions from the β decay of laser-trapped 6He atoms

NASA Astrophysics Data System (ADS)

Hong, R.; Leredde, A.; Bagdasarova, Y.; Fléchard, X.; García, A.; Knecht, A.; Müller, P.; Naviliat-Cuncic, O.; Pedersen, J.; Smith, E.; Sternberg, M.; Storm, D. Â. W.; Swanson, H. Â. E.; Wauters, F.; Zumwalt, D.

2017-11-01

The accurate determination of atomic final states following nuclear β decay plays an important role in several experiments. In particular, the charge state distributions of ions following nuclear β decay are important for determinations of the β -ν angular correlation with improved precision. Beyond the hydrogenic cases, the decay of neutral 6He presents the simplest case. Our measurement aims at providing benchmarks to test theoretical calculations. The kinematics of Lin + ions produced following the β decay of 6He within an electric field were measured using 6He atoms in the metastable (1 s 2 s ,S31) and (1 s 2 p ,P32) states confined by a magneto-optical trap. The electron shakeoff probabilities were deduced, including their dependence on ion energy. We find significant discrepancies on the fractions of Li ions in the different charge states with respect to a recent calculation.

A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

NASA Astrophysics Data System (ADS)

Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

2017-04-01

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Sexual differentiation in the distribution potential of northern jaguars (Panthera onca)

USGS Publications Warehouse

Boydston, Erin E.; Lopez Gonzalez, Carlos A.

2005-01-01

We estimated the potential geographic distribution of jaguars in the southwestern United States and northwestern Mexico by modeling the jaguar ecological niche from occurrence records. We modeled separately the distribution of males and females, assuming records of females probably represented established home ranges while male records likely included dispersal movements. The predicted distribution for males was larger than that for females. Eastern Sonora appeared capable for supporting male and female jaguars with potential range expansion into southeastern Arizona. New Mexico and Chihuahua contained environmental characteristics primarily limited to the male niche and thus may be areas into which males occasionally disperse.

Computer models of social processes: the case of migration.

PubMed

Beshers, J M

1967-06-01

The demographic model is a program for representing births, deaths, migration, and social mobility as social processes in a non-stationary stochastic process (Markovian). Transition probabilities for each age group are stored and then retrieved at the next appearance of that age cohort. In this way new transition probabilities can be calculated as a function of the old transition probabilities and of two successive distribution vectors.Transition probabilities can be calculated to represent effects of the whole age-by-state distribution at any given time period, too. Such effects as saturation or queuing may be represented by a market mechanism; for example, migration between metropolitan areas can be represented as depending upon job supplies and labor markets. Within metropolitan areas, migration can be represented as invasion and succession processes with tipping points (acceleration curves), and the market device has been extended to represent this phenomenon.Thus, the demographic model makes possible the representation of alternative classes of models of demographic processes. With each class of model one can deduce implied time series (varying parame-terswithin the class) and the output of the several classes can be compared to each other and to outside criteria, such as empirical time series.

Investigation of Dielectric Breakdown Characteristics for Double-break Vacuum Interrupter and Dielectric Breakdown Probability Distribution in Vacuum Interrupter

NASA Astrophysics Data System (ADS)

Shioiri, Tetsu; Asari, Naoki; Sato, Junichi; Sasage, Kosuke; Yokokura, Kunio; Homma, Mitsutaka; Suzuki, Katsumi

To investigate the reliability of equipment of vacuum insulation, a study was carried out to clarify breakdown probability distributions in vacuum gap. Further, a double-break vacuum circuit breaker was investigated for breakdown probability distribution. The test results show that the breakdown probability distribution of the vacuum gap can be represented by a Weibull distribution using a location parameter, which shows the voltage that permits a zero breakdown probability. The location parameter obtained from Weibull plot depends on electrode area. The shape parameter obtained from Weibull plot of vacuum gap was 10∼14, and is constant irrespective non-uniform field factor. The breakdown probability distribution after no-load switching can be represented by Weibull distribution using a location parameter. The shape parameter after no-load switching was 6∼8.5, and is constant, irrespective of gap length. This indicates that the scatter of breakdown voltage was increased by no-load switching. If the vacuum circuit breaker uses a double break, breakdown probability at low voltage becomes lower than single-break probability. Although potential distribution is a concern in the double-break vacuum cuicuit breaker, its insulation reliability is better than that of the single-break vacuum interrupter even if the bias of the vacuum interrupter's sharing voltage is taken into account.

Non-Gaussian elliptic-flow fluctuations in PbPb collisions at $$\\sqrt{\\smash[b]{s_{_\\text{NN}}}} = 5.02$$ TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sirunyan, Albert M; et al.

Event-by-event fluctuations in the elliptic-flow coefficientmore » $$v_2$$ are studied in PbPb collisions at $$\\sqrt{s_{_\\text{NN}}} = 5.02$$ TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions $${p}(v_2)$$ for charged particles with transverse momentum 0.3$$< p_\\mathrm{T} <$$3.0 GeV and pseudorapidity $$| \\eta | <$$ 1.0 are determined for different collision centrality classes. The moments of the $${p}(v_2)$$ distributions are used to calculate the $$v_{2}$$ coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the $${p}(v_2)$$ distributions indicate non-Gaussian initial-state fluctuation behavior. Bessel-Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy.« less

Using a Betabinomial distribution to estimate the prevalence of adherence to physical activity guidelines among children and youth.

PubMed

Garriguet, Didier

2016-04-01

Estimates of the prevalence of adherence to physical activity guidelines in the population are generally the result of averaging individual probability of adherence based on the number of days people meet the guidelines and the number of days they are assessed. Given this number of active and inactive days (days assessed minus days active), the conditional probability of meeting the guidelines that has been used in the past is a Beta (1 + active days, 1 + inactive days) distribution assuming the probability p of a day being active is bounded by 0 and 1 and averages 50%. A change in the assumption about the distribution of p is required to better match the discrete nature of the data and to better assess the probability of adherence when the percentage of active days in the population differs from 50%. Using accelerometry data from the Canadian Health Measures Survey, the probability of adherence to physical activity guidelines is estimated using a conditional probability given the number of active and inactive days distributed as a Betabinomial(n, a + active days , β + inactive days) assuming that p is randomly distributed as Beta(a, β) where the parameters a and β are estimated by maximum likelihood. The resulting Betabinomial distribution is discrete. For children aged 6 or older, the probability of meeting physical activity guidelines 7 out of 7 days is similar to published estimates. For pre-schoolers, the Betabinomial distribution yields higher estimates of adherence to the guidelines than the Beta distribution, in line with the probability of being active on any given day. In estimating the probability of adherence to physical activity guidelines, the Betabinomial distribution has several advantages over the previously used Beta distribution. It is a discrete distribution and maximizes the richness of accelerometer data.

[Probabilistic calculations of biomolecule charge states that generate mass spectra of multiply charged ions].

PubMed

Raznikova, M O; Raznikov, V V

2015-01-01

In this work, information relating to charge states of biomolecule ions in solution obtained using the electrospray ionization mass spectrometry of different biopolymers is analyzed. The data analyses have mainly been carried out by solving an inverse problem of calculating the probabilities of retention of protons and other charge carriers by ionogenic groups of biomolecules with known primary structures. The approach is a new one and has no known to us analogues. A program titled "Decomposition" was developed and used to analyze the charge distribution of ions of native and denatured cytochrome c mass spectra. The possibility of splitting of the charge-state distribution of albumin into normal components, which likely corresponds to various conformational states of the biomolecule, has been demonstrated. The applicability criterion for using previously described method of decomposition of multidimensional charge-state distributions with two charge carriers, e.g., a proton and a sodium ion, to characterize the spatial structure of biopolymers in solution has been formulated. In contrast to known mass-spectrometric approaches, this method does not require the use of enzymatic hydrolysis or collision-induced dissociation of the biopolymers.

Stochastic analysis of a pulse-type prey-predator model

NASA Astrophysics Data System (ADS)

Wu, Y.; Zhu, W. Q.

2008-04-01

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

Stochastic analysis of a pulse-type prey-predator model.

PubMed

Wu, Y; Zhu, W Q

2008-04-01

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

Gravity and count probabilities in an expanding universe

NASA Technical Reports Server (NTRS)

Bouchet, Francois R.; Hernquist, Lars

1992-01-01

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Analytical approach to impurity transport studies: Charge state dynamics in tokamak plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shurygin, V. A.

2006-08-15

Ionization and recombination of plasma impurities govern their charge state kinetics, which is imposed upon the dynamics of ions that implies a superposition of the appropriate probabilities and causes an impurity charge state dynamics. The latter is considered in terms of a vector field of conditional probabilities and presented by a vector charge state distribution function with coupled equations of the Kolmogorov type. Analytical solutions of a diffusion problem are derived with the basic spatial and temporal dimensionless parameters. Analysis shows that the empirical scaling D{sub A}{proportional_to}n{sub e}{sup -1} [K. Krieger, G. Fussmann, and the ASDEX Upgrade Team, Nucl. Fusionmore » 30, 2392 (1990)] can be explained by the ratio of the diffusive and kinetic terms, D{sub A}/(n{sub e}a{sup 2}), being used instead of diffusivity, D{sub A}. The derived time scales of charge state dynamics are given by a sum of the diffusive and kinetic times. Detailed simulations of charge state dynamics are performed for argon impurity and compared with the reference modeling.« less

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

NASA Astrophysics Data System (ADS)

Donkov, Sava; Stefanov, Ivan Z.

2018-03-01

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a non-linear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to an equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

Microscopic modeling of gas-surface scattering: II. Application to argon atom adsorption on a platinum (111) surface

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A new combination of first principle molecular dynamics (MD) simulations with a rate equation model presented in the preceding paper (paper I) is applied to analyze in detail the scattering of argon atoms from a platinum (111) surface. The combined model is based on a classification of all atom trajectories according to their energies into trapped, quasi-trapped and scattering states. The number of particles in each of the three classes obeys coupled rate equations. The coefficients in the rate equations are the transition probabilities between these states which are obtained from MD simulations. While these rates are generally time-dependent, after a characteristic time scale t E of several tens of picoseconds they become stationary allowing for a rather simple analysis. Here, we investigate this time scale by analyzing in detail the temporal evolution of the energy distribution functions of the adsorbate atoms. We separately study the energy loss distribution function of the atoms and the distribution function of in-plane and perpendicular energy components. Further, we compute the sticking probability of argon atoms as a function of incident energy, angle and lattice temperature. Our model is important for plasma-surface modeling as it allows to extend accurate simulations to longer time scales.

Event dependence in U.S. executions

PubMed Central

Baumgartner, Frank R.; Box-Steffensmeier, Janet M.

2018-01-01

Since 1976, the United States has seen over 1,400 judicial executions, and these have been highly concentrated in only a few states and counties. The number of executions across counties appears to fit a stretched distribution. These distributions are typically reflective of self-reinforcing processes where the probability of observing an event increases for each previous event. To examine these processes, we employ two-pronged empirical strategy. First, we utilize bootstrapped Kolmogorov-Smirnov tests to determine whether the pattern of executions reflect a stretched distribution, and confirm that they do. Second, we test for event-dependence using the Conditional Frailty Model. Our tests estimate the monthly hazard of an execution in a given county, accounting for the number of previous executions, homicides, poverty, and population demographics. Controlling for other factors, we find that the number of prior executions in a county increases the probability of the next execution and accelerates its timing. Once a jurisdiction goes down a given path, the path becomes self-reinforcing, causing the counties to separate out into those never executing (the vast majority of counties) and those which use the punishment frequently. This finding is of great legal and normative concern, and ultimately, may not be consistent with the equal protection clause of the U.S. Constitution. PMID:29293583

Slip-Size Distribution and Self-Organized Criticality in Block-Spring Models with Quenched Randomness

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Kadowaki, Shuntaro

2017-07-01

We study slowly pulling block-spring models in random media. Second-order phase transitions exist in a model pulled by a constant force in the case of velocity-strengthening friction. If external forces are slowly increased, nearly critical states are self-organized. Slips of various sizes occur, and the probability distributions of slip size roughly obey power laws. The exponent is close to that in the quenched Edwards-Wilkinson model. Furthermore, the slip-size distributions are investigated in cases of Coulomb friction, velocity-weakening friction, and two-dimensional block-spring models.

Explosion probability of unexploded ordnance: expert beliefs.

PubMed

MacDonald, Jacqueline Anne; Small, Mitchell J; Morgan, M G

2008-08-01

This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies are needed to better understand the explosion risks of UXO.

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

NASA Astrophysics Data System (ADS)

Zhang, Hongda; Han, Chao; Ye, Taohong; Ren, Zhuyin

2016-03-01

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.

Spin polarization and magnetic dichroism in photoemission from core and valence states in localized magnetic systems. IV. Core-hole polarization in resonant photoemission

NASA Astrophysics Data System (ADS)

van der Laan, Gerrit; Thole, B. T.

1995-12-01

A simple theory is presented for core-hole polarization probed by resonant photoemission in a two-steps approximation. After excitation from a core level to the valence shell, the core hole decays into two shallower core holes under emission of an electron. The nonspherical core hole and the final state selected cause a specific angle and spin distribution of the emitted electron. The experiment is characterized by the ground-state moments, the polarization of the light, and the spin and angular distribution of the emitted electron. The intensity is a sum over ground-state expectation values of tensor operators times the probability to create a polarized core hole using polarized light, times the probability for decay of such a core hole into the final state. We give general expressions for the angle- and spin-dependent intensities in various regimes of Coulomb and spin-orbit interaction: LS, LSJ, and jjJ coupling. The core-polarization analysis, which generalizes the use of sum rules in x-ray absorption spectroscopy where the integrated peak intensities give ground-state expectation values of the spin and orbital moment operators, makes it possible to measure different linear combinations of these operators. As an application the 2p3/23p3p decay in ferromagnetic nickel is calculated using Hartree-Fock values for the radial matrix elements and phase factors, and compared with experiment, the dichroism is smaller in the 3P final state but stronger in the 1D, 1S peak.

Sampling design trade-offs in occupancy studies with imperfect detection: examples and software

USGS Publications Warehouse

Bailey, L.L.; Hines, J.E.; Nichols, J.D.

2007-01-01

Researchers have used occupancy, or probability of occupancy, as a response or state variable in a variety of studies (e.g., habitat modeling), and occupancy is increasingly favored by numerous state, federal, and international agencies engaged in monitoring programs. Recent advances in estimation methods have emphasized that reliable inferences can be made from these types of studies if detection and occupancy probabilities are simultaneously estimated. The need for temporal replication at sampled sites to estimate detection probability creates a trade-off between spatial replication (number of sample sites distributed within the area of interest/inference) and temporal replication (number of repeated surveys at each site). Here, we discuss a suite of questions commonly encountered during the design phase of occupancy studies, and we describe software (program GENPRES) developed to allow investigators to easily explore design trade-offs focused on particularities of their study system and sampling limitations. We illustrate the utility of program GENPRES using an amphibian example from Greater Yellowstone National Park, USA.

Dynamics in atomic signaling games.

PubMed

Fox, Michael J; Touri, Behrouz; Shamma, Jeff S

2015-07-07

We study an atomic signaling game under stochastic evolutionary dynamics. There are a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss. Copyright © 2015 Elsevier Ltd. All rights reserved.

Distinguishing computable mixtures of quantum states

NASA Astrophysics Data System (ADS)

Grande, Ignacio H. López; Senno, Gabriel; de la Torre, Gonzalo; Larotonda, Miguel A.; Bendersky, Ariel; Figueira, Santiago; Acín, Antonio

2018-05-01

In this article we extend results from our previous work [Bendersky et al., Phys. Rev. Lett. 116, 230402 (2016), 10.1103/PhysRevLett.116.230402] by providing a protocol to distinguish in finite time and with arbitrarily high success probability any algorithmic mixture of pure states from the maximally mixed state. Moreover, we include an experimental realization, using a modified quantum key distribution setup, where two different random sequences of pure states are prepared; these sequences are indistinguishable according to quantum mechanics, but they become distinguishable when randomness is replaced with pseudorandomness within the experimental preparation process.

Principle of maximum entropy for reliability analysis in the design of machine components

NASA Astrophysics Data System (ADS)

Zhang, Yimin

2018-03-01

We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects.

Target Tracking Using SePDAF under Ambiguous Angles for Distributed Array Radar.

PubMed

Long, Teng; Zhang, Honggang; Zeng, Tao; Chen, Xinliang; Liu, Quanhua; Zheng, Le

2016-09-09

Distributed array radar can improve radar detection capability and measurement accuracy. However, it will suffer cyclic ambiguity in its angle estimates according to the spatial Nyquist sampling theorem since the large sparse array is undersampling. Consequently, the state estimation accuracy and track validity probability degrades when the ambiguous angles are directly used for target tracking. This paper proposes a second probability data association filter (SePDAF)-based tracking method for distributed array radar. Firstly, the target motion model and radar measurement model is built. Secondly, the fusion result of each radar's estimation is employed to the extended Kalman filter (EKF) to finish the first filtering. Thirdly, taking this result as prior knowledge, and associating with the array-processed ambiguous angles, the SePDAF is applied to accomplish the second filtering, and then achieving a high accuracy and stable trajectory with relatively low computational complexity. Moreover, the azimuth filtering accuracy will be promoted dramatically and the position filtering accuracy will also improve. Finally, simulations illustrate the effectiveness of the proposed method.

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation.

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Role of social environment and social clustering in spread of opinions in coevolving networks.

PubMed

Malik, Nishant; Mucha, Peter J

2013-12-01

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the coevolving network voter model of opinion formation studied by Holme and Newman [Phys. Rev. E 74, 056108 (2006)]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for heterogeneity and asymmetric influences in relationships between individuals. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus, allowing for the existence of diverse opinions, and the other having a single dominant connected component with each node within that dominant component having the same opinion. Furthermore, more importantly, we found that the initial clustering in the network can also induce similar transitions. Our investigation also indicates that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes.

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

NASA Astrophysics Data System (ADS)

Schwalger, Tilo; Lindner, Benjamin

2015-12-01

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.

PubMed

Dinov, Ivo D; Siegrist, Kyle; Pearl, Dennis K; Kalinin, Alexandr; Christou, Nicolas

2016-06-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome , which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions

PubMed Central

Dinov, Ivo D.; Siegrist, Kyle; Pearl, Dennis K.; Kalinin, Alexandr; Christou, Nicolas

2015-01-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome, which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols. PMID:27158191

Random Partition Distribution Indexed by Pairwise Information

PubMed Central

Dahl, David B.; Day, Ryan; Tsai, Jerry W.

2017-01-01

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution. PMID:29276318

A brief introduction to probability.

PubMed

Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio

2018-02-01

The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with four-intensity decoy-state method.

PubMed

Mao, Chen-Chen; Zhou, Xing-Yu; Zhu, Jian-Rong; Zhang, Chun-Hui; Zhang, Chun-Mei; Wang, Qin

2018-05-14

Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation analysis.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

PubMed

Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter

2012-01-01

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

Human variability in mercury toxicokinetics and steady state biomarker ratios.

PubMed

Bartell, S M; Ponce, R A; Sanga, R N; Faustman, E M

2000-10-01

Regulatory guidelines regarding methylmercury exposure depend on dose-response models relating observed mercury concentrations in maternal blood, cord blood, and maternal hair to developmental neurobehavioral endpoints. Generalized estimates of the maternal blood-to-hair, blood-to-intake, or hair-to-intake ratios are necessary for linking exposure to biomarker-based dose-response models. Most assessments have used point estimates for these ratios; however, significant interindividual and interstudy variability has been reported. For example, a maternal ratio of 250 ppm in hair per mg/L in blood is commonly used in models, but a 1990 WHO review reports mean ratios ranging from 140 to 370 ppm per mg/L. To account for interindividual and interstudy variation in applying these ratios to risk and safety assessment, some researchers have proposed representing the ratios with probability distributions and conducting probabilistic assessments. Such assessments would allow regulators to consider the range and like-lihood of mercury exposures in a population, rather than limiting the evaluation to an estimate of the average exposure or a single conservative exposure estimate. However, no consensus exists on the most appropriate distributions for representing these parameters. We discuss published reviews of blood-to-hair and blood-to-intake steady state ratios for mercury and suggest statistical approaches for combining existing datasets to form generalized probability distributions for mercury distribution ratios. Although generalized distributions may not be applicable to all populations, they allow a more informative assessment than point estimates where individual biokinetic information is unavailable. Whereas development and use of these distributions will improve existing exposure and risk models, additional efforts in data generation and model development are required.

Cortical Dynamics in Presence of Assemblies of Densely Connected Weight-Hub Neurons

PubMed Central

Setareh, Hesam; Deger, Moritz; Petersen, Carl C. H.; Gerstner, Wulfram

2017-01-01

Experimental measurements of pairwise connection probability of pyramidal neurons together with the distribution of synaptic weights have been used to construct randomly connected model networks. However, several experimental studies suggest that both wiring and synaptic weight structure between neurons show statistics that differ from random networks. Here we study a network containing a subset of neurons which we call weight-hub neurons, that are characterized by strong inward synapses. We propose a connectivity structure for excitatory neurons that contain assemblies of densely connected weight-hub neurons, while the pairwise connection probability and synaptic weight distribution remain consistent with experimental data. Simulations of such a network with generalized integrate-and-fire neurons display regular and irregular slow oscillations akin to experimentally observed up/down state transitions in the activity of cortical neurons with a broad distribution of pairwise spike correlations. Moreover, stimulation of a model network in the presence or absence of assembly structure exhibits responses similar to light-evoked responses of cortical layers in optogenetically modified animals. We conclude that a high connection probability into and within assemblies of excitatory weight-hub neurons, as it likely is present in some but not all cortical layers, changes the dynamics of a layer of cortical microcircuitry significantly. PMID:28690508

Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Simulating landscape change in the Olympic Peninsula using spatial ecological and socioeconomic data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flamm, R.O.; Gottfried, R.; Lee, R.G.

1994-06-01

Ecological and socioeconomic data were integrated to study landscape change for the Dungeness River basin in the Olympic Peninsula, Washington State. A multinomial logit procedure was used to evaluate twenty-two maps representing various data themes to derive transition probabilities of land cover change. Probabilities of forest disturbance were greater on private land than public. Between 1975 and 1988, forest cover increased, grassy/brushy covers decreased, and the number of forest patches increased about 30%. Simulations were run to estimate future land cover. These results were represented as frequency distributions for proportion cover and patch characteristics.

Analysis of HIV-1 intersubtype recombination breakpoints suggests region with high pairing probability may be a more fundamental factor than sequence similarity affecting HIV-1 recombination.

PubMed

Jia, Lei; Li, Lin; Gui, Tao; Liu, Siyang; Li, Hanping; Han, Jingwan; Guo, Wei; Liu, Yongjian; Li, Jingyun

2016-09-21

With increasing data on HIV-1, a more relevant molecular model describing mechanism details of HIV-1 genetic recombination usually requires upgrades. Currently an incomplete structural understanding of the copy choice mechanism along with several other issues in the field that lack elucidation led us to perform an analysis of the correlation between breakpoint distributions and (1) the probability of base pairing, and (2) intersubtype genetic similarity to further explore structural mechanisms. Near full length sequences of URFs from Asia, Europe, and Africa (one sequence/patient), and representative sequences of worldwide CRFs were retrieved from the Los Alamos HIV database. Their recombination patterns were analyzed by jpHMM in detail. Then the relationships between breakpoint distributions and (1) the probability of base pairing, and (2) intersubtype genetic similarities were investigated. Pearson correlation test showed that all URF groups and the CRF group exhibit the same breakpoint distribution pattern. Additionally, the Wilcoxon two-sample test indicated a significant and inexplicable limitation of recombination in regions with high pairing probability. These regions have been found to be strongly conserved across distinct biological states (i.e., strong intersubtype similarity), and genetic similarity has been determined to be a very important factor promoting recombination. Thus, the results revealed an unexpected disagreement between intersubtype similarity and breakpoint distribution, which were further confirmed by genetic similarity analysis. Our analysis reveals a critical conflict between results from natural HIV-1 isolates and those from HIV-1-based assay vectors in which genetic similarity has been shown to be a very critical factor promoting recombination. These results indicate the region with high-pairing probabilities may be a more fundamental factor affecting HIV-1 recombination than sequence similarity in natural HIV-1 infections. Our findings will be relevant in furthering the understanding of HIV-1 recombination mechanisms.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

Combined-probability space and certainty or uncertainty relations for a finite-level quantum system

NASA Astrophysics Data System (ADS)

Sehrawat, Arun

2017-08-01

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

The global impact distribution of Near-Earth objects

NASA Astrophysics Data System (ADS)

Rumpf, Clemens; Lewis, Hugh G.; Atkinson, Peter M.

2016-02-01

Asteroids that could collide with the Earth are listed on the publicly available Near-Earth object (NEO) hazard web sites maintained by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The impact probability distribution of 69 potentially threatening NEOs from these lists that produce 261 dynamically distinct impact instances, or Virtual Impactors (VIs), were calculated using the Asteroid Risk Mitigation and Optimization Research (ARMOR) tool in conjunction with OrbFit. ARMOR projected the impact probability of each VI onto the surface of the Earth as a spatial probability distribution. The projection considers orbit solution accuracy and the global impact probability. The method of ARMOR is introduced and the tool is validated against two asteroid-Earth collision cases with objects 2008 TC3 and 2014 AA. In the analysis, the natural distribution of impact corridors is contrasted against the impact probability distribution to evaluate the distributions' conformity with the uniform impact distribution assumption. The distribution of impact corridors is based on the NEO population and orbital mechanics. The analysis shows that the distribution of impact corridors matches the common assumption of uniform impact distribution and the result extends the evidence base for the uniform assumption from qualitative analysis of historic impact events into the future in a quantitative way. This finding is confirmed in a parallel analysis of impact points belonging to a synthetic population of 10,006 VIs. Taking into account the impact probabilities introduced significant variation into the results and the impact probability distribution, consequently, deviates markedly from uniformity. The concept of impact probabilities is a product of the asteroid observation and orbit determination technique and, thus, represents a man-made component that is largely disconnected from natural processes. It is important to consider impact probabilities because such information represents the best estimate of where an impact might occur.

Meaner king uses biased bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reimpell, Michael; Werner, Reinhard F.

2007-06-15

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases aremore » mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell's original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.« less

Meaner king uses biased bases

NASA Astrophysics Data System (ADS)

Reimpell, Michael; Werner, Reinhard F.

2007-06-01

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell’s original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.

Spectrocopic measurements of water vapor plasmas at high resolution: The optical transition probabilities for OH (A 2 Sigma - X 2 Pi)

NASA Technical Reports Server (NTRS)

Klein, L.

1972-01-01

Emission and absorption spectra of water vapor plasmas generated in a wall-stabilized arc at atmospheric pressure and 4 current, and at 0.03 atm and 15 to 50 A, were measured at high spatial and spectral resolution. The gas temperature was determined from the shape of Doppler-broadened rotational lines of OH. The observed nonequilibrium population distributions over the energy levels of atoms are interpreted in terms of a theoretical state model for diffusion-controlled arc plasmas. Excellent correlation is achieved between measured and predicted occupation of hydrogen energy levels. It is shown that the population distribution over the nonpredissociating rotational-vibrational levels of the A 2 Sigma state of OH is close to an equilibrium distribution at the gas temperature, although the total density of this state is much higher than its equilibrium density. The reduced intensities of the rotational lines originating in these levels yielded Boltzmann plots that were strictly linear.

Uncertainty analysis in fault tree models with dependent basic events.

PubMed

Pedroni, Nicola; Zio, Enrico

2013-06-01

In general, two types of dependence need to be considered when estimating the probability of the top event (TE) of a fault tree (FT): "objective" dependence between the (random) occurrences of different basic events (BEs) in the FT and "state-of-knowledge" (epistemic) dependence between estimates of the epistemically uncertain probabilities of some BEs of the FT model. In this article, we study the effects on the TE probability of objective and epistemic dependences. The well-known Frèchet bounds and the distribution envelope determination (DEnv) method are used to model all kinds of (possibly unknown) objective and epistemic dependences, respectively. For exemplification, the analyses are carried out on a FT with six BEs. Results show that both types of dependence significantly affect the TE probability; however, the effects of epistemic dependence are likely to be overwhelmed by those of objective dependence (if present). © 2012 Society for Risk Analysis.

Cost-effective solutions to maintaining smart grid reliability

NASA Astrophysics Data System (ADS)

Qin, Qiu

As the aging power systems are increasingly working closer to the capacity and thermal limits, maintaining an sufficient reliability has been of great concern to the government agency, utility companies and users. This dissertation focuses on improving the reliability of transmission and distribution systems. Based on the wide area measurements, multiple model algorithms are developed to diagnose transmission line three-phase short to ground faults in the presence of protection misoperations. The multiple model algorithms utilize the electric network dynamics to provide prompt and reliable diagnosis outcomes. Computational complexity of the diagnosis algorithm is reduced by using a two-step heuristic. The multiple model algorithm is incorporated into a hybrid simulation framework, which consist of both continuous state simulation and discrete event simulation, to study the operation of transmission systems. With hybrid simulation, line switching strategy for enhancing the tolerance to protection misoperations is studied based on the concept of security index, which involves the faulted mode probability and stability coverage. Local measurements are used to track the generator state and faulty mode probabilities are calculated in the multiple model algorithms. FACTS devices are considered as controllers for the transmission system. The placement of FACTS devices into power systems is investigated with a criterion of maintaining a prescribed level of control reconfigurability. Control reconfigurability measures the small signal combined controllability and observability of a power system with an additional requirement on fault tolerance. For the distribution systems, a hierarchical framework, including a high level recloser allocation scheme and a low level recloser placement scheme, is presented. The impacts of recloser placement on the reliability indices is analyzed. Evaluation of reliability indices in the placement process is carried out via discrete event simulation. The reliability requirements are described with probabilities and evaluated from the empirical distributions of reliability indices.

A Computer Simulation Using Spreadsheets for Learning Concept of Steady-State Equilibrium

ERIC Educational Resources Information Center

Sharda, Vandana; Sastri, O. S. K. S.; Bhardwaj, Jyoti; Jha, Arbind K.

2016-01-01

In this paper, we present a simple spreadsheet based simulation activity that can be performed by students at the undergraduate level. This simulation is implemented in free open source software (FOSS) LibreOffice Calc, which is available for both Windows and Linux platform. This activity aims at building the probability distribution for the…

Methylmercury Poisoning—An Assessment of the Sportfish Hazard in California

PubMed Central

Dales, Loring; Kahn, Ephraim; Wei, Eddie

1971-01-01

A quantitative assessment of the methylmercury risk in California entails measurement of the contamination distribution, the probability of methylmercury intake and knowledge of the toxicological properties of methylmercury. This article reviews the scientific basis for the California State Task Force's decision to warn the public against excessive consumption of sport fish contaminated by methylmercury. PMID:5544687

Teacher Quality and Teacher Mobility. Working Paper 57

ERIC Educational Resources Information Center

Feng, Li; Sass, Tim

2011-01-01

Using matched student-teacher panel data from the state of Florida, the authors study the determinants of teacher job change and the impact of such mobility on the distribution of teacher quality. The probability a teacher stays at a school increases the more productive they are in their current school. The quality of teachers who exit teaching…

Modeling habitat dynamics accounting for possible misclassification

USGS Publications Warehouse

Veran, Sophie; Kleiner, Kevin J.; Choquet, Remi; Collazo, Jaime; Nichols, James D.

2012-01-01

Land cover data are widely used in ecology as land cover change is a major component of changes affecting ecological systems. Landscape change estimates are characterized by classification errors. Researchers have used error matrices to adjust estimates of areal extent, but estimation of land cover change is more difficult and more challenging, with error in classification being confused with change. We modeled land cover dynamics for a discrete set of habitat states. The approach accounts for state uncertainty to produce unbiased estimates of habitat transition probabilities using ground information to inform error rates. We consider the case when true and observed habitat states are available for the same geographic unit (pixel) and when true and observed states are obtained at one level of resolution, but transition probabilities estimated at a different level of resolution (aggregations of pixels). Simulation results showed a strong bias when estimating transition probabilities if misclassification was not accounted for. Scaling-up does not necessarily decrease the bias and can even increase it. Analyses of land cover data in the Southeast region of the USA showed that land change patterns appeared distorted if misclassification was not accounted for: rate of habitat turnover was artificially increased and habitat composition appeared more homogeneous. Not properly accounting for land cover misclassification can produce misleading inferences about habitat state and dynamics and also misleading predictions about species distributions based on habitat. Our models that explicitly account for state uncertainty should be useful in obtaining more accurate inferences about change from data that include errors.

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knessl, C.; Tier, C.

1999-10-01

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Lévy noise improves the electrical activity in a neuron under electromagnetic radiation.

PubMed

Wu, Juan; Xu, Yong; Ma, Jun

2017-01-01

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Lévy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Lévy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Lévy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Lévy noise intensity are depicted. The increasing of Lévy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Lévy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Lévy noise distribution are detected.

Lévy noise improves the electrical activity in a neuron under electromagnetic radiation

PubMed Central

Wu, Juan; Ma, Jun

2017-01-01

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Lévy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Lévy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Lévy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Lévy noise intensity are depicted. The increasing of Lévy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Lévy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Lévy noise distribution are detected. PMID:28358824

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks.

PubMed

Meng, X Flora; Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M

2017-05-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. © 2017 The Author(s).

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

PubMed Central

Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M.

2017-01-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. PMID:28566513

Stimulated luminescence emission from localized recombination in randomly distributed defects.

PubMed

Jain, Mayank; Guralnik, Benny; Andersen, Martin Thalbitzer

2012-09-26

We present a new kinetic model describing localized electronic recombination through the excited state of the donor (d) to an acceptor (a) centre in luminescent materials. In contrast to the existing models based on the localized transition model (LTM) of Halperin and Braner (1960 Phys. Rev. 117 408-15) which assumes a fixed d → a tunnelling probability for the entire crystal, our model is based on nearest-neighbour recombination within randomly distributed centres. Such a random distribution can occur through the entire volume or within the defect complexes of the dosimeter, and implies that the tunnelling probability varies with the donor-acceptor (d-a) separation distance. We first develop an 'exact kinetic model' that incorporates this variation in tunnelling probabilities, and evolves both in spatial as well as temporal domains. We then develop a simplified one-dimensional, semi-analytical model that evolves only in the temporal domain. An excellent agreement is observed between thermally and optically stimulated luminescence (TL and OSL) results produced from the two models. In comparison to the first-order kinetic behaviour of the LTM of Halperin and Braner (1960 Phys. Rev. 117 408-15), our model results in a highly asymmetric TL peak; this peak can be understood to derive from a continuum of several first-order TL peaks. Our model also shows an extended power law behaviour for OSL (or prompt luminescence), which is expected from localized recombination mechanisms in materials with random distribution of centres.

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com; Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in; Pathak, Anirban, E-mail: anirban.pathak@gmail.com

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained frommore » experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.« less

Charge-state distribution of Li ions from the β decay of laser-trapped He 6 atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, R.; Leredde, A.; Bagdasarova, Y.

The accurate determination of atomic final states following nuclear β decay plays an important role in several experiments. In particular, the charge state distributions of ions following nuclear β decay are important for determinations of the β-ν angular correlation with improved precision. Also, beyond the hydrogenic cases, the decay of neutral 6He presents the simplest case. Our measurement aims at providing benchmarks to test theoretical calculations. The kinematics of Li n+ ions produced following the β decay of 6He within an electric field were measured using 6He atoms in the metastable (1s2s, 3S 1) and (1s2p, 3P 2) states confinedmore » by a magneto-optical trap. The electron shakeoff probabilities were deduced, including their dependence on ion energy. Finally, we find significant discrepancies on the fractions of Li ions in the different charge states with respect to a recent calculation.« less

Charge-state distribution of Li ions from the β decay of laser-trapped He 6 atoms

DOE PAGES

Hong, R.; Leredde, A.; Bagdasarova, Y.; ...

2017-11-13

The accurate determination of atomic final states following nuclear β decay plays an important role in several experiments. In particular, the charge state distributions of ions following nuclear β decay are important for determinations of the β-ν angular correlation with improved precision. Also, beyond the hydrogenic cases, the decay of neutral 6He presents the simplest case. Our measurement aims at providing benchmarks to test theoretical calculations. The kinematics of Li n+ ions produced following the β decay of 6He within an electric field were measured using 6He atoms in the metastable (1s2s, 3S 1) and (1s2p, 3P 2) states confinedmore » by a magneto-optical trap. The electron shakeoff probabilities were deduced, including their dependence on ion energy. Finally, we find significant discrepancies on the fractions of Li ions in the different charge states with respect to a recent calculation.« less

Nonadditive entropies yield probability distributions with biases not warranted by the data.

PubMed

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A

2013-11-01

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.

Axionic landscape for Higgs coupling near-criticality

NASA Astrophysics Data System (ADS)

Cline, James M.; Espinosa, José R.

2018-02-01

The measured value of the Higgs quartic coupling λ is peculiarly close to the critical value above which the Higgs potential becomes unstable, when extrapolated to high scales by renormalization group running. It is tempting to speculate that there is an anthropic reason behind this near-criticality. We show how an axionic field can provide a landscape of vacuum states in which λ scans. These states are populated during inflation to create a multiverse with different quartic couplings, with a probability distribution P that can be computed. If P is peaked in the anthropically forbidden region of Higgs instability, then the most probable universe compatible with observers would be close to the boundary, as observed. We discuss three scenarios depending on the Higgs vacuum selection mechanism: decay by quantum tunneling, by thermal fluctuations, or by inflationary fluctuations.

Anomalous finite-size effects in the Battle of the Sexes

NASA Astrophysics Data System (ADS)

Cremer, J.; Reichenbach, T.; Frey, E.

2008-06-01

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

NASA Astrophysics Data System (ADS)

Robbins, Matthew P. G.

Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.

Probabilistic self-organizing maps for continuous data.

PubMed

Lopez-Rubio, Ezequiel

2010-10-01

The original self-organizing feature map did not define any probability distribution on the input space. However, the advantages of introducing probabilistic methodologies into self-organizing map models were soon evident. This has led to a wide range of proposals which reflect the current emergence of probabilistic approaches to computational intelligence. The underlying estimation theories behind them derive from two main lines of thought: the expectation maximization methodology and stochastic approximation methods. Here, we present a comprehensive view of the state of the art, with a unifying perspective of the involved theoretical frameworks. In particular, we examine the most commonly used continuous probability distributions, self-organization mechanisms, and learning schemes. Special emphasis is given to the connections among them and their relative advantages depending on the characteristics of the problem at hand. Furthermore, we evaluate their performance in two typical applications of self-organizing maps: classification and visualization.

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling.

PubMed

Richard, David; Speck, Thomas

2018-03-28

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

NASA Astrophysics Data System (ADS)

Richard, David; Speck, Thomas

2018-03-01

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

César Mansur Filho, Júlio; Dickman, Ronald

2011-05-01

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\

Lattice gas models for particle systems in an underdamped hopping regime

NASA Astrophysics Data System (ADS)

Gobron, Thierry

A model in which the state of the particle is described by a multicomponent vector, each possible kinetic state for the particle being associated with one of the components is presented. A master equation describes the evolution of the probability distribution in an independent particle model. From the master equation and with the help of the symmetry group that leaves the state transition operator invariant, physical quantities such as the diffusion constant are explicitly calculated for several lattices in one, two, and three dimensions. A Boltzmann equation is established and compared to the Rice and Roth proposal.

ProbOnto: ontology and knowledge base of probability distributions.

PubMed

Swat, Maciej J; Grenon, Pierre; Wimalaratne, Sarala

2016-09-01

Probability distributions play a central role in mathematical and statistical modelling. The encoding, annotation and exchange of such models could be greatly simplified by a resource providing a common reference for the definition of probability distributions. Although some resources exist, no suitably detailed and complex ontology exists nor any database allowing programmatic access. ProbOnto, is an ontology-based knowledge base of probability distributions, featuring more than 80 uni- and multivariate distributions with their defining functions, characteristics, relationships and re-parameterization formulas. It can be used for model annotation and facilitates the encoding of distribution-based models, related functions and quantities. http://probonto.org mjswat@ebi.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

NASA Astrophysics Data System (ADS)

de Oliveira, M. M.; da Luz, M. G. E.; Fiore, C. E.

2015-12-01

Based on quasistationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as response functions, cumulants, and equal area probability distributions all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions—to single and infinitely many absorbing states—are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasistationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to a unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.

Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerrits, Thomas; Stevens, Martin; Baek, Burm

We characterize a periodically poled KTP crystal that produces an entangled, two-mode, squeezed state with orthogonal polarizations, nearly identical, factorizable frequency modes, and few photons in unwanted frequency modes. We focus the pump beam to create a nearly circular joint spectral probability distribution between the two modes. After disentangling the two modes, we observe Hong-Ou-Mandel interference with a raw (background corrected) visibility of 86% (95%) when an 8.6 nm bandwidth spectral filter is applied. We measure second order photon correlations of the entangled and disentangled squeezed states with both superconducting nanowire single-photon detectors and photon-number-resolving transition-edge sensors. Both methods agreemore » and verify that the detected modes contain the desired photon number distributions.« less

Maps showing gas-hydrate distribution off the east coast of the United States

USGS Publications Warehouse

Dillon, William P.; Fehlhaber, Kristen L.; Coleman, Dwight F.; Lee, Myung W.; Hutchinson, Deborah R.

1995-01-01

These maps present the inferred distribution of natural-gas hydrate within the sediments of the eastern United States continental margin (Exclusive Economic Zone) in the offshore region from Georgia to New Jersey (fig. 1). The maps, which were created on the basis of seismic interpretations, represent the first attempt to map volume estimates for gas hydrate. Gas hydrate forms a large reservoir for methane in oceanic sediments. Therefore it potentially may represent a future source of energy and it may influence climate change because methane is a very effective greenhouse gas. Hydrate breakdown probably is a controlling factor for sea-floor landslides, and its presence has significant effect on the acoustic velocity of sea-floor sediments.

Comparision of the different probability distributions for earthquake hazard assessment in the North Anatolian Fault Zone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com; Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr

In this study we examined and compared the three different probabilistic distribution methods for determining the best suitable model in probabilistic assessment of earthquake hazards. We analyzed a reliable homogeneous earthquake catalogue between a time period 1900-2015 for magnitude M ≥ 6.0 and estimated the probabilistic seismic hazard in the North Anatolian Fault zone (39°-41° N 30°-40° E) using three distribution methods namely Weibull distribution, Frechet distribution and three-parameter Weibull distribution. The distribution parameters suitability was evaluated Kolmogorov-Smirnov (K-S) goodness-of-fit test. We also compared the estimated cumulative probability and the conditional probabilities of occurrence of earthquakes for different elapsed timemore » using these three distribution methods. We used Easyfit and Matlab software to calculate these distribution parameters and plotted the conditional probability curves. We concluded that the Weibull distribution method was the most suitable than other distribution methods in this region.« less

Importance-sampling computation of statistical properties of coupled oscillators

NASA Astrophysics Data System (ADS)

Gupta, Shamik; Leitão, Jorge C.; Altmann, Eduardo G.

2017-07-01

We introduce and implement an importance-sampling Monte Carlo algorithm to study systems of globally coupled oscillators. Our computational method efficiently obtains estimates of the tails of the distribution of various measures of dynamical trajectories corresponding to states occurring with (exponentially) small probabilities. We demonstrate the general validity of our results by applying the method to two contrasting cases: the driven-dissipative Kuramoto model, a paradigm in the study of spontaneous synchronization; and the conservative Hamiltonian mean-field model, a prototypical system of long-range interactions. We present results for the distribution of the finite-time Lyapunov exponent and a time-averaged order parameter. Among other features, our results show most notably that the distributions exhibit a vanishing standard deviation but a skewness that is increasing in magnitude with the number of oscillators, implying that nontrivial asymmetries and states yielding rare or atypical values of the observables persist even for a large number of oscillators.

Statistical Analysis of Spectral Properties and Prosodic Parameters of Emotional Speech

NASA Astrophysics Data System (ADS)

Přibil, J.; Přibilová, A.

2009-01-01

The paper addresses reflection of microintonation and spectral properties in male and female acted emotional speech. Microintonation component of speech melody is analyzed regarding its spectral and statistical parameters. According to psychological research of emotional speech, different emotions are accompanied by different spectral noise. We control its amount by spectral flatness according to which the high frequency noise is mixed in voiced frames during cepstral speech synthesis. Our experiments are aimed at statistical analysis of cepstral coefficient values and ranges of spectral flatness in three emotions (joy, sadness, anger), and a neutral state for comparison. Calculated histograms of spectral flatness distribution are visually compared and modelled by Gamma probability distribution. Histograms of cepstral coefficient distribution are evaluated and compared using skewness and kurtosis. Achieved statistical results show good correlation comparing male and female voices for all emotional states portrayed by several Czech and Slovak professional actors.

Probabilistic graphs as a conceptual and computational tool in hydrology and water management

NASA Astrophysics Data System (ADS)

Schoups, Gerrit

2014-05-01

Originally developed in the fields of machine learning and artificial intelligence, probabilistic graphs constitute a general framework for modeling complex systems in the presence of uncertainty. The framework consists of three components: 1. Representation of the model as a graph (or network), with nodes depicting random variables in the model (e.g. parameters, states, etc), which are joined together by factors. Factors are local probabilistic or deterministic relations between subsets of variables, which, when multiplied together, yield the joint distribution over all variables. 2. Consistent use of probability theory for quantifying uncertainty, relying on basic rules of probability for assimilating data into the model and expressing unknown variables as a function of observations (via the posterior distribution). 3. Efficient, distributed approximation of the posterior distribution using general-purpose algorithms that exploit model structure encoded in the graph. These attributes make probabilistic graphs potentially useful as a conceptual and computational tool in hydrology and water management (and beyond). Conceptually, they can provide a common framework for existing and new probabilistic modeling approaches (e.g. by drawing inspiration from other fields of application), while computationally they can make probabilistic inference feasible in larger hydrological models. The presentation explores, via examples, some of these benefits.

Incorporating Skew into RMS Surface Roughness Probability Distribution

NASA Technical Reports Server (NTRS)

Stahl, Mark T.; Stahl, H. Philip.

2013-01-01

The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.

Bayesian microsaccade detection

PubMed Central

Mihali, Andra; van Opheusden, Bas; Ma, Wei Ji

2017-01-01

Microsaccades are high-velocity fixational eye movements, with special roles in perception and cognition. The default microsaccade detection method is to determine when the smoothed eye velocity exceeds a threshold. We have developed a new method, Bayesian microsaccade detection (BMD), which performs inference based on a simple statistical model of eye positions. In this model, a hidden state variable changes between drift and microsaccade states at random times. The eye position is a biased random walk with different velocity distributions for each state. BMD generates samples from the posterior probability distribution over the eye state time series given the eye position time series. Applied to simulated data, BMD recovers the “true” microsaccades with fewer errors than alternative algorithms, especially at high noise. Applied to EyeLink eye tracker data, BMD detects almost all the microsaccades detected by the default method, but also apparent microsaccades embedded in high noise—although these can also be interpreted as false positives. Next we apply the algorithms to data collected with a Dual Purkinje Image eye tracker, whose higher precision justifies defining the inferred microsaccades as ground truth. When we add artificial measurement noise, the inferences of all algorithms degrade; however, at noise levels comparable to EyeLink data, BMD recovers the “true” microsaccades with 54% fewer errors than the default algorithm. Though unsuitable for online detection, BMD has other advantages: It returns probabilities rather than binary judgments, and it can be straightforwardly adapted as the generative model is refined. We make our algorithm available as a software package. PMID:28114483

Combining state-and-transition simulations and species distribution models to anticipate the effects of climate change

USGS Publications Warehouse

Miller, Brian W.; Frid, Leonardo; Chang, Tony; Piekielek, N. B.; Hansen, Andrew J.; Morisette, Jeffrey T.

2015-01-01

State-and-transition simulation models (STSMs) are known for their ability to explore the combined effects of multiple disturbances, ecological dynamics, and management actions on vegetation. However, integrating the additional impacts of climate change into STSMs remains a challenge. We address this challenge by combining an STSM with species distribution modeling (SDM). SDMs estimate the probability of occurrence of a given species based on observed presence and absence locations as well as environmental and climatic covariates. Thus, in order to account for changes in habitat suitability due to climate change, we used SDM to generate continuous surfaces of species occurrence probabilities. These data were imported into ST-Sim, an STSM platform, where they dictated the probability of each cell transitioning between alternate potential vegetation types at each time step. The STSM was parameterized to capture additional processes of vegetation growth and disturbance that are relevant to a keystone species in the Greater Yellowstone Ecosystem—whitebark pine (Pinus albicaulis). We compared historical model runs against historical observations of whitebark pine and a key disturbance agent (mountain pine beetle, Dendroctonus ponderosae), and then projected the simulation into the future. Using this combination of correlative and stochastic simulation models, we were able to reproduce historical observations and identify key data gaps. Results indicated that SDMs and STSMs are complementary tools, and combining them is an effective way to account for the anticipated impacts of climate change, biotic interactions, and disturbances, while also allowing for the exploration of management options.

Quantum Walks on the Line with Phase Parameters

NASA Astrophysics Data System (ADS)

Villagra, Marcos; Nakanishi, Masaki; Yamashita, Shigeru; Nakashima, Yasuhiko

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general SU(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric SU(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.

A Markov Environment-dependent Hurricane Intensity Model and Its Comparison with Multiple Dynamic Models

NASA Astrophysics Data System (ADS)

Jing, R.; Lin, N.; Emanuel, K.; Vecchi, G. A.; Knutson, T. R.

2017-12-01

A Markov environment-dependent hurricane intensity model (MeHiM) is developed to simulate the climatology of hurricane intensity given the surrounding large-scale environment. The model considers three unobserved discrete states representing respectively storm's slow, moderate, and rapid intensification (and deintensification). Each state is associated with a probability distribution of intensity change. The storm's movement from one state to another, regarded as a Markov chain, is described by a transition probability matrix. The initial state is estimated with a Bayesian approach. All three model components (initial intensity, state transition, and intensity change) are dependent on environmental variables including potential intensity, vertical wind shear, midlevel relative humidity, and ocean mixing characteristics. This dependent Markov model of hurricane intensity shows a significant improvement over previous statistical models (e.g., linear, nonlinear, and finite mixture models) in estimating the distributions of 6-h and 24-h intensity change, lifetime maximum intensity, and landfall intensity, etc. Here we compare MeHiM with various dynamical models, including a global climate model [High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR)], a regional hurricane model (Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model), and a simplified hurricane dynamic model [Coupled Hurricane Intensity Prediction System (CHIPS)] and its newly developed fast simulator. The MeHiM developed based on the reanalysis data is applied to estimate the intensity of simulated storms to compare with the dynamical-model predictions under the current climate. The dependences of hurricanes on the environment under current and future projected climates in the various models will also be compared statistically.

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

Vertical changes in the probability distribution of downward irradiance within the near-surface ocean under sunny conditions

NASA Astrophysics Data System (ADS)

Gernez, Pierre; Stramski, Dariusz; Darecki, Miroslaw

2011-07-01

Time series measurements of fluctuations in underwater downward irradiance, Ed, within the green spectral band (532 nm) show that the probability distribution of instantaneous irradiance varies greatly as a function of depth within the near-surface ocean under sunny conditions. Because of intense light flashes caused by surface wave focusing, the near-surface probability distributions are highly skewed to the right and are heavy tailed. The coefficients of skewness and excess kurtosis at depths smaller than 1 m can exceed 3 and 20, respectively. We tested several probability models, such as lognormal, Gumbel, Fréchet, log-logistic, and Pareto, which are potentially suited to describe the highly skewed heavy-tailed distributions. We found that the models cannot approximate with consistently good accuracy the high irradiance values within the right tail of the experimental distribution where the probability of these values is less than 10%. This portion of the distribution corresponds approximately to light flashes with Ed > 1.5?, where ? is the time-averaged downward irradiance. However, the remaining part of the probability distribution covering all irradiance values smaller than the 90th percentile can be described with a reasonable accuracy (i.e., within 20%) with a lognormal model for all 86 measurements from the top 10 m of the ocean included in this analysis. As the intensity of irradiance fluctuations decreases with depth, the probability distribution tends toward a function symmetrical around the mean like the normal distribution. For the examined data set, the skewness and excess kurtosis assumed values very close to zero at a depth of about 10 m.

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows.

PubMed

Dobramysl, U; Holcman, D

2018-02-15

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

How extreme was the October 2015 flood in the Carolinas? An assessment of flood frequency analysis and distribution tails

NASA Astrophysics Data System (ADS)

Phillips, R. C.; Samadi, S. Z.; Meadows, M. E.

2018-07-01

This paper examines the frequency, distribution tails, and peak-over-threshold (POT) of extreme floods through analysis that centers on the October 2015 flooding in North Carolina (NC) and South Carolina (SC), United States (US). The most striking features of the October 2015 flooding were a short time to peak (Tp) and a multi-hour continuous flood peak which caused intensive and widespread damages to human lives, properties, and infrastructure. The 2015 flooding was produced by a sequence of intense rainfall events which originated from category 4 hurricane Joaquin over a period of four days. Here, the probability distribution and distribution parameters (i.e., location, scale, and shape) of floods were investigated by comparing the upper part of empirical distributions of the annual maximum flood (AMF) and POT with light- to heavy- theoretical tails: Fréchet, Pareto, Gumbel, Weibull, Beta, and Exponential. Specifically, four sets of U.S. Geological Survey (USGS) gauging data from the central Carolinas with record lengths from approximately 65-125 years were used. Analysis suggests that heavier-tailed distributions are in better agreement with the POT and somewhat AMF data than more often used exponential (light) tailed probability distributions. Further, the threshold selection and record length affect the heaviness of the tail and fluctuations of the parent distributions. The shape parameter and its evolution in the period of record play a critical and poorly understood role in determining the scaling of flood response to intense rainfall.

Investigation of excited states populations density of Hall thruster plasma in three dimensions by laser-induced fluorescence spectroscopy

NASA Astrophysics Data System (ADS)

Krivoruchko, D. D.; Skrylev, A. V.

2018-01-01

The article deals with investigation of the excited states populations distribution of a low-temperature xenon plasma in the thruster with closed electron drift at 300 W operating conditions were investigated by laser-induced fluorescence (LIF) over the 350-1100 nm range. Seven xenon ions (Xe II) transitions were analyzed, while for neutral atoms (Xe I) just three transitions were explored, since the majority of Xe I emission falls into the ultraviolet or infrared part of the spectrum and are difficult to measure. The necessary spontaneous emission probabilities (Einstein coefficients) were calculated. Measurements of the excited state distribution were made for points (volume of about 12 mm3) all over the plane perpendicular to thruster axis in four positions on it (5, 10, 50 and 100 mm). Measured LIF signal intensity have differences for each location of researched point (due to anisotropy of thruster plume), however the structure of states populations distribution persisted at plume and is violated at the thruster exit plane and cathode area. Measured distributions show that for describing plasma of Hall thruster one needs to use a multilevel kinetic model, classic model can be used just for far plume region or for specific electron transitions.

Impact of signal scattering and parametric uncertainties on receiver operating characteristics

NASA Astrophysics Data System (ADS)

Wilson, D. Keith; Breton, Daniel J.; Hart, Carl R.; Pettit, Chris L.

2017-05-01

The receiver operating characteristic (ROC curve), which is a plot of the probability of detection as a function of the probability of false alarm, plays a key role in the classical analysis of detector performance. However, meaningful characterization of the ROC curve is challenging when practically important complications such as variations in source emissions, environmental impacts on the signal propagation, uncertainties in the sensor response, and multiple sources of interference are considered. In this paper, a relatively simple but realistic model for scattered signals is employed to explore how parametric uncertainties impact the ROC curve. In particular, we show that parametric uncertainties in the mean signal and noise power substantially raise the tails of the distributions; since receiver operation with a very low probability of false alarm and a high probability of detection is normally desired, these tails lead to severely degraded performance. Because full a priori knowledge of such parametric uncertainties is rarely available in practice, analyses must typically be based on a finite sample of environmental states, which only partially characterize the range of parameter variations. We show how this effect can lead to misleading assessments of system performance. For the cases considered, approximately 64 or more statistically independent samples of the uncertain parameters are needed to accurately predict the probabilities of detection and false alarm. A connection is also described between selection of suitable distributions for the uncertain parameters, and Bayesian adaptive methods for inferring the parameters.

Rogue waves in a multistable system.

PubMed

Pisarchik, Alexander N; Jaimes-Reátegui, Rider; Sevilla-Escoboza, Ricardo; Huerta-Cuellar, G; Taki, Majid

2011-12-30

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.

The Renner effect in triatomic molecules with application to CH+, MgNC and NH2.

PubMed

Jensen, Per; Odaka, Tina Erica; Kraemer, W P; Hirano, Tsuneo; Bunker, P R

2002-03-01

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(p) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f+(rho) and f-(rho) associated with the individual Born-Oppenheimer states phi(-)elec and phi(+)elec. At a given temperature the Boltzmann averaged value of the f(p) over all the eigenstates gives the bending probability distribution function F(rho), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH2+, MgNC and NH2, all of which are of astrophysical interest.

Predicting the probability of slip in gait: methodology and distribution study.

PubMed

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.

Integrated-Circuit Pseudorandom-Number Generator

NASA Technical Reports Server (NTRS)

Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur

1992-01-01

Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

Thermodynamic method for generating random stress distributions on an earthquake fault

USGS Publications Warehouse

Barall, Michael; Harris, Ruth A.

2012-01-01

This report presents a new method for generating random stress distributions on an earthquake fault, suitable for use as initial conditions in a dynamic rupture simulation. The method employs concepts from thermodynamics and statistical mechanics. A pattern of fault slip is considered to be analogous to a micro-state of a thermodynamic system. The energy of the micro-state is taken to be the elastic energy stored in the surrounding medium. Then, the Boltzmann distribution gives the probability of a given pattern of fault slip and stress. We show how to decompose the system into independent degrees of freedom, which makes it computationally feasible to select a random state. However, due to the equipartition theorem, straightforward application of the Boltzmann distribution leads to a divergence which predicts infinite stress. To avoid equipartition, we show that the finite strength of the fault acts to restrict the possible states of the system. By analyzing a set of earthquake scaling relations, we derive a new formula for the expected power spectral density of the stress distribution, which allows us to construct a computer algorithm free of infinities. We then present a new technique for controlling the extent of the rupture by generating a random stress distribution thousands of times larger than the fault surface, and selecting a portion which, by chance, has a positive stress perturbation of the desired size. Finally, we present a new two-stage nucleation method that combines a small zone of forced rupture with a larger zone of reduced fracture energy.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Meng-Zheng; School of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000; Ye, Liu, E-mail: yeliu@ahu.edu.cn

An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC)more » transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.« less

Target Tracking Using SePDAF under Ambiguous Angles for Distributed Array Radar

PubMed Central

Long, Teng; Zhang, Honggang; Zeng, Tao; Chen, Xinliang; Liu, Quanhua; Zheng, Le

2016-01-01

Distributed array radar can improve radar detection capability and measurement accuracy. However, it will suffer cyclic ambiguity in its angle estimates according to the spatial Nyquist sampling theorem since the large sparse array is undersampling. Consequently, the state estimation accuracy and track validity probability degrades when the ambiguous angles are directly used for target tracking. This paper proposes a second probability data association filter (SePDAF)-based tracking method for distributed array radar. Firstly, the target motion model and radar measurement model is built. Secondly, the fusion result of each radar’s estimation is employed to the extended Kalman filter (EKF) to finish the first filtering. Thirdly, taking this result as prior knowledge, and associating with the array-processed ambiguous angles, the SePDAF is applied to accomplish the second filtering, and then achieving a high accuracy and stable trajectory with relatively low computational complexity. Moreover, the azimuth filtering accuracy will be promoted dramatically and the position filtering accuracy will also improve. Finally, simulations illustrate the effectiveness of the proposed method. PMID:27618058

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

Development and application of a probability distribution retrieval scheme to the remote sensing of clouds and precipitation

NASA Astrophysics Data System (ADS)

McKague, Darren Shawn

2001-12-01

The statistical properties of clouds and precipitation on a global scale are important to our understanding of climate. Inversion methods exist to retrieve the needed cloud and precipitation properties from satellite data pixel-by-pixel that can then be summarized over large data sets to obtain the desired statistics. These methods can be quite computationally expensive, and typically don't provide errors on the statistics. A new method is developed to directly retrieve probability distributions of parameters from the distribution of measured radiances. The method also provides estimates of the errors on the retrieved distributions. The method can retrieve joint distributions of parameters that allows for the study of the connection between parameters. A forward radiative transfer model creates a mapping from retrieval parameter space to radiance space. A Monte Carlo procedure uses the mapping to transform probability density from the observed radiance histogram to a two- dimensional retrieval property probability distribution function (PDF). An estimate of the uncertainty in the retrieved PDF is calculated from random realizations of the radiance to retrieval parameter PDF transformation given the uncertainty of the observed radiances, the radiance PDF, the forward radiative transfer, the finite number of prior state vectors, and the non-unique mapping to retrieval parameter space. The retrieval method is also applied to the remote sensing of precipitation from SSM/I microwave data. A method of stochastically generating hydrometeor fields based on the fields from a numerical cloud model is used to create the precipitation parameter radiance space transformation. The impact of vertical and horizontal variability within the hydrometeor fields has a significant impact on algorithm performance. Beamfilling factors are computed from the simulated hydrometeor fields. The beamfilling factors vary quite a bit depending upon the horizontal structure of the rain. The algorithm is applied to SSM/I images from the eastern tropical Pacific and is compared to PDFs of rain rate computed using pixel-by-pixel retrievals from Wilheit and from Liu and Curry. Differences exist between the three methods, but good general agreement is seen between the PDF retrieval algorithm and the algorithm of Liu and Curry. (Abstract shortened by UMI.)

Conditional probability distribution function of "energy transfer rate" (PDF(ɛ|PVI)) as compared with its counterpart of temperature (PDF(T|PVI)) at the same condition of fluctuation

NASA Astrophysics Data System (ADS)

He, Jiansen; Wang, Yin; Pei, Zhongtian; Zhang, Lei; Tu, Chuanyi

2017-04-01

Energy transfer rate of turbulence is not uniform everywhere but suggested to follow a certain distribution, e.g., lognormal distribution (Kolmogorov 1962). The inhomogeneous transfer rate leads to emergence of intermittency, which may be identified with some parameter, e.g., normalized partial variance increments (PVI) (Greco et al., 2009). Large PVI of magnetic field fluctuations are found to have a temperature distribution with the median and mean values higher than that for small PVI level (Osman et al., 2012). However, there is a large proportion of overlap between temperature distributions associated with the smaller and larger PVIs. So it is recognized that only PVI cannot fully determine the temperature, since the one-to-one mapping relationship does not exist. One may be curious about the reason responsible for the considerable overlap of conditional temperature distribution for different levels of PVI. Usually the hotter plasma with higher temperature is speculated to be heated more with more dissipation of turbulence energy corresponding to more energy cascading rate, if the temperature fluctuation of the eigen wave mode is not taken into account. To explore the statistical relationship between turbulence cascading and plasma thermal state, we aim to study and reveal, for the first time, the conditional probability function of "energy transfer rate" under different levels of PVI condition (PDF(ɛ|PVI)), and compare it with the conditional probability function of temperature. The conditional probability distribution function, PDF(ɛ|PVI), is derived from PDF(PVI|ɛ)·PDF(ɛ)/PDF(PVI) according to the Bayesian theorem. PDF(PVI) can be obtained directly from the data. PDF(ɛ) is derived from the conjugate-gradient inversion of PDF(PVI) by assuming reasonably that PDF(δB|σ) is a Gaussian distribution, where PVI=|δB|/ σ and σ ( ɛι)1/3. PDF(ɛ) can also be acquired from fitting PDF(δB) with an integral function ∫PDF(δB|σ)PDF(σ)d σ. As a result, PDF(ɛ|PVI) is found to shift to higher median value of ɛ with increasing PVI but with a significant overlap of PDFs for different PVIs. Therefore, PDF(ɛ|PVI) is similar to PDF(T|PVI) in the sense of slow migration along with increasing PVI. The detailed comparison between these two conditional PDFs are also performed.

Stochastic Computations in Cortical Microcircuit Models

PubMed Central

Maass, Wolfgang

2013-01-01

Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving. PMID:24244126

Two-state theory of binned photon statistics for a large class of waiting time distributions and its application to quantum dot blinking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volkán-Kacsó, Sándor

2014-06-14

A theoretical method is proposed for the calculation of the photon counting probability distribution during a bin time. Two-state fluorescence and steady excitation are assumed. A key feature is a kinetic scheme that allows for an extensive class of stochastic waiting time distribution functions, including power laws, expanded as a sum of weighted decaying exponentials. The solution is analytic in certain conditions, and an exact and simple expression is found for the integral contribution of “bright” and “dark” states. As an application for power law kinetics, theoretical results are compared with experimental intensity histograms from a number of blinking CdSe/ZnSmore » quantum dots. The histograms are consistent with distributions of intensity states around a “bright” and a “dark” maximum. A gap of states is also revealed in the more-or-less flat inter-peak region. The slope and to some extent the flatness of the inter-peak feature are found to be sensitive to the power-law exponents. Possible models consistent with these findings are discussed, such as the combination of multiple charging and fluctuating non-radiative channels or the multiple recombination center model. A fitting of the latter to experiment provides constraints on the interaction parameter between the recombination centers. Further extensions and applications of the photon counting theory are also discussed.« less

Periodic synchronization in a system of coupled phase oscillators with attractive and repulsive interactions

NASA Astrophysics Data System (ADS)

Yuan, Di; Tian, Jun-Long; Lin, Fang; Ma, Dong-Wei; Zhang, Jing; Cui, Hai-Tao; Xiao, Yi

2018-06-01

In this study we investigate the collective behavior of the generalized Kuramoto model with an external pinning force in which oscillators with positive and negative coupling strengths are conformists and contrarians, respectively. We focus on a situation in which the natural frequencies of the oscillators follow a uniform probability density. By numerically simulating the model, it is shown that the model supports multistable synchronized states such as a traveling wave state, π state and periodic synchronous state: an oscillating π state. The oscillating π state may be characterized by the phase distribution oscillating in a confined region and the phase difference between conformists and contrarians oscillating around π periodically. In addition, we present the parameter space of the oscillating π state and traveling wave state of the model.

Statistical Neurodynamics.

NASA Astrophysics Data System (ADS)

Paine, Gregory Harold

1982-03-01

The primary objective of the thesis is to explore the dynamical properties of small nerve networks by means of the methods of statistical mechanics. To this end, a general formalism is developed and applied to elementary groupings of model neurons which are driven by either constant (steady state) or nonconstant (nonsteady state) forces. Neuronal models described by a system of coupled, nonlinear, first-order, ordinary differential equations are considered. A linearized form of the neuronal equations is studied in detail. A Lagrange function corresponding to the linear neural network is constructed which, through a Legendre transformation, provides a constant of motion. By invoking the Maximum-Entropy Principle with the single integral of motion as a constraint, a probability distribution function for the network in a steady state can be obtained. The formalism is implemented for some simple networks driven by a constant force; accordingly, the analysis focuses on a study of fluctuations about the steady state. In particular, a network composed of N noninteracting neurons, termed Free Thinkers, is considered in detail, with a view to interpretation and numerical estimation of the Lagrange multiplier corresponding to the constant of motion. As an archetypical example of a net of interacting neurons, the classical neural oscillator, consisting of two mutually inhibitory neurons, is investigated. It is further shown that in the case of a network driven by a nonconstant force, the Maximum-Entropy Principle can be applied to determine a probability distribution functional describing the network in a nonsteady state. The above examples are reconsidered with nonconstant driving forces which produce small deviations from the steady state. Numerical studies are performed on simplified models of two physical systems: the starfish central nervous system and the mammalian olfactory bulb. Discussions are given as to how statistical neurodynamics can be used to gain a better understanding of the behavior of these systems.

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.; Ashwworth, G. R.; Winter, W. R.

1980-01-01

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Experimental non-classicality of an indivisible quantum system.

PubMed

Lapkiewicz, Radek; Li, Peizhe; Schaeff, Christoph; Langford, Nathan K; Ramelow, Sven; Wieśniak, Marcin; Zeilinger, Anton

2011-06-22

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Assessment of source probabilities for potential tsunamis affecting the U.S. Atlantic coast

USGS Publications Warehouse

Geist, E.L.; Parsons, T.

2009-01-01

Estimating the likelihood of tsunamis occurring along the U.S. Atlantic coast critically depends on knowledge of tsunami source probability. We review available information on both earthquake and landslide probabilities from potential sources that could generate local and transoceanic tsunamis. Estimating source probability includes defining both size and recurrence distributions for earthquakes and landslides. For the former distribution, source sizes are often distributed according to a truncated or tapered power-law relationship. For the latter distribution, sources are often assumed to occur in time according to a Poisson process, simplifying the way tsunami probabilities from individual sources can be aggregated. For the U.S. Atlantic coast, earthquake tsunami sources primarily occur at transoceanic distances along plate boundary faults. Probabilities for these sources are constrained from previous statistical studies of global seismicity for similar plate boundary types. In contrast, there is presently little information constraining landslide probabilities that may generate local tsunamis. Though there is significant uncertainty in tsunami source probabilities for the Atlantic, results from this study yield a comparative analysis of tsunami source recurrence rates that can form the basis for future probabilistic analyses.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

The adventive status of Salvinia minima and S. molestain the southern United States and the related distribution of the weevil Cyrtobagous salviniae

USGS Publications Warehouse

Jacono, Colette C.; Davern, Tracy R.; Center, Ted D.

2001-01-01

The recent introduction of Salvinia molesta constitutes a serious threat to aquatic systems in the warm temperate regions of the United States. Salvinia minima, the only other member of Salviniaceae present in North America, is considered native by current floras. Evidence is presented which suggests that Salvinia minima was also introduced to North America, probably during the late 1920s and early 1930s. Likely sites of introduction and subsequent range expansions are identified. The accidentally introduced salvinia weevil, putatively Cyrtobagous salviniae, was found to occur widely on S. minima in Florida but is not established in other states. The disparate distribution of this Salvinia herbivore may account for the reduced aggressiveness of S. minima in Florida as compared to its troublesome growth in Texas and LOUisiana, where the weevil is not yet known.

The H2 + + He proton transfer reaction: quantum reactive differential cross sections to be linked with future velocity mapping experiments

NASA Astrophysics Data System (ADS)

Hernández Vera, Mario; Wester, Roland; Gianturco, Francesco Antonio

2018-01-01

We construct the velocity map images of the proton transfer reaction between helium and molecular hydrogen ion {{{H}}}2+. We perform simulations of imaging experiments at one representative total collision energy taking into account the inherent aberrations of the velocity mapping in order to explore the feasibility of direct comparisons between theory and future experiments planned in our laboratory. The asymptotic angular distributions of the fragments in a 3D velocity space is determined from the quantum state-to-state differential reactive cross sections and reaction probabilities which are computed by using the time-independent coupled channel hyperspherical coordinate method. The calculations employ an earlier ab initio potential energy surface computed at the FCI/cc-pVQZ level of theory. The present simulations indicate that the planned experiments would be selective enough to differentiate between product distributions resulting from different initial internal states of the reactants.

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

Statistical physics of medical diagnostics: Study of a probabilistic model.

PubMed

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

Statistical physics of medical diagnostics: Study of a probabilistic model

NASA Astrophysics Data System (ADS)

Mashaghi, Alireza; Ramezanpour, Abolfazl

2018-03-01

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.

Ubiquity of Benford's law and emergence of the reciprocal distribution

DOE PAGES

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

2016-04-07

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

Climate controls the distribution of a widespread invasive species: Implications for future range expansion

USGS Publications Warehouse

McDowell, W.G.; Benson, A.J.; Byers, J.E.

2014-01-01

1. Two dominant drivers of species distributions are climate and habitat, both of which are changing rapidly. Understanding the relative importance of variables that can control distributions is critical, especially for invasive species that may spread rapidly and have strong effects on ecosystems. 2. Here, we examine the relative importance of climate and habitat variables in controlling the distribution of the widespread invasive freshwater clam Corbicula fluminea, and we model its future distribution under a suite of climate scenarios using logistic regression and maximum entropy modelling (MaxEnt). 3. Logistic regression identified climate variables as more important than habitat variables in controlling Corbicula distribution. MaxEnt modelling predicted Corbicula's range expansion westward and northward to occupy half of the contiguous United States. By 2080, Corbicula's potential range will expand 25–32%, with more than half of the continental United States being climatically suitable. 4. Our combination of multiple approaches has revealed the importance of climate over habitat in controlling Corbicula's distribution and validates the climate-only MaxEnt model, which can readily examine the consequences of future climate projections. 5. Given the strong influence of climate variables on Corbicula's distribution, as well as Corbicula's ability to disperse quickly and over long distances, Corbicula is poised to expand into New England and the northern Midwest of the United States. Thus, the direct effects of climate change will probably be compounded by the addition of Corbicula and its own influences on ecosystem function.

Spatial Probability Distribution of Strata's Lithofacies and its Impacts on Land Subsidence in Huairou Emergency Water Resources Region of Beijing

NASA Astrophysics Data System (ADS)

Li, Y.; Gong, H.; Zhu, L.; Guo, L.; Gao, M.; Zhou, C.

2016-12-01

Continuous over-exploitation of groundwater causes dramatic drawdown, and leads to regional land subsidence in the Huairou Emergency Water Resources region, which is located in the up-middle part of the Chaobai river basin of Beijing. Owing to the spatial heterogeneity of strata's lithofacies of the alluvial fan, ground deformation has no significant positive correlation with groundwater drawdown, and one of the challenges ahead is to quantify the spatial distribution of strata's lithofacies. The transition probability geostatistics approach provides potential for characterizing the distribution of heterogeneous lithofacies in the subsurface. Combined the thickness of clay layer extracted from the simulation, with deformation field acquired from PS-InSAR technology, the influence of strata's lithofacies on land subsidence can be analyzed quantitatively. The strata's lithofacies derived from borehole data were generalized into four categories and their probability distribution in the observe space was mined by using the transition probability geostatistics, of which clay was the predominant compressible material. Geologically plausible realizations of lithofacies distribution were produced, accounting for complex heterogeneity in alluvial plain. At a particular probability level of more than 40 percent, the volume of clay defined was 55 percent of the total volume of strata's lithofacies. This level, equaling nearly the volume of compressible clay derived from the geostatistics, was thus chosen to represent the boundary between compressible and uncompressible material. The method incorporates statistical geological information, such as distribution proportions, average lengths and juxtaposition tendencies of geological types, mainly derived from borehole data and expert knowledge, into the Markov chain model of transition probability. Some similarities of patterns were indicated between the spatial distribution of deformation field and clay layer. In the area with roughly similar water table decline, locations in the subsurface having a higher probability for the existence of compressible material occur more than that in the location with a lower probability. Such estimate of spatial probability distribution is useful to analyze the uncertainty of land subsidence.

The exact probability distribution of the rank product statistics for replicated experiments.

PubMed

Eisinga, Rob; Breitling, Rainer; Heskes, Tom

2013-03-18

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Climate Change Impact Assessment in Pacific North West Using Copula based Coupling of Temperature and Precipitation variables

NASA Astrophysics Data System (ADS)

Qin, Y.; Rana, A.; Moradkhani, H.

2014-12-01

The multi downscaled-scenario products allow us to better assess the uncertainty of the changes/variations of precipitation and temperature in the current and future periods. Joint Probability distribution functions (PDFs), of both the climatic variables, might help better understand the interdependence of the two, and thus in-turn help in accessing the future with confidence. Using the joint distribution of temperature and precipitation is also of significant importance in hydrological applications and climate change studies. In the present study, we have used multi-modelled statistically downscaled-scenario ensemble of precipitation and temperature variables using 2 different statistically downscaled climate dataset. The datasets used are, 10 Global Climate Models (GCMs) downscaled products from CMIP5 daily dataset, namely, those from the Bias Correction and Spatial Downscaling (BCSD) technique generated at Portland State University and from the Multivariate Adaptive Constructed Analogs (MACA) technique, generated at University of Idaho, leading to 2 ensemble time series from 20 GCM products. Thereafter the ensemble PDFs of both precipitation and temperature is evaluated for summer, winter, and yearly periods for all the 10 sub-basins across Columbia River Basin (CRB). Eventually, Copula is applied to establish the joint distribution of two variables enabling users to model the joint behavior of the variables with any level of correlation and dependency. Moreover, the probabilistic distribution helps remove the limitations on marginal distributions of variables in question. The joint distribution is then used to estimate the change trends of the joint precipitation and temperature in the current and future, along with estimation of the probabilities of the given change. Results have indicated towards varied change trends of the joint distribution of, summer, winter, and yearly time scale, respectively in all 10 sub-basins. Probabilities of changes, as estimated by the joint precipitation and temperature, will provide useful information/insights for hydrological and climate change predictions.

Convergence Time and Phase Transition in a Non-monotonic Family of Probabilistic Cellular Automata

NASA Astrophysics Data System (ADS)

Ramos, A. D.; Leite, A.

2017-08-01

In dynamical systems, some of the most important questions are related to phase transitions and convergence time. We consider a one-dimensional probabilistic cellular automaton where their components assume two possible states, zero and one, and interact with their two nearest neighbors at each time step. Under the local interaction, if the component is in the same state as its two neighbors, it does not change its state. In the other cases, a component in state zero turns into a one with probability α , and a component in state one turns into a zero with probability 1-β . For certain values of α and β , we show that the process will always converge weakly to δ 0, the measure concentrated on the configuration where all the components are zeros. Moreover, the mean time of this convergence is finite, and we describe an upper bound in this case, which is a linear function of the initial distribution. We also demonstrate an application of our results to the percolation PCA. Finally, we use mean-field approximation and Monte Carlo simulations to show coexistence of three distinct behaviours for some values of parameters α and β.

Genetic structure of Culex erraticus populations across the Americas.

PubMed

Mendenhall, Ian H; Bahl, Justin; Blum, Michael J; Wesson, Dawn M

2012-05-01

Culex erraticus (Dyar & Knab) is a potential competent vector for several arboviruses such as Eastern and Venezuelan equine encephalitis viruses and West Nile virus. It therefore may play a role in the maintenance and spread of viral populations in areas of concern, including the United States where it occurs in >33 states. However, little information is available on potential barriers to movement across the species' distribution. Here, we analyze genetic variation among Cx. erraticus collected from Colombia, Guatemala, and nine locations in the United States to better understand population structure and connectivity. Comparative sequence analysis of the second internal transcribed spacer and mitochondrial NADH dehydrogenase genes identified two major lineages of sampled populations. One lineage represented the central and eastern United States, whereas the other corresponded to Central America, South America, and the western United States. Hierarchical analysis of genetic variation provided further evidence of regional population structure, although the majority of genetic variation was found to reside within populations, suggestive of large population sizes. Although significant physical barriers such as the Chihuahuan Desert probably constrain the spread of Cx. erraticus, large population sizes and connectivity within regions remain important risk factors that probably contribute to the movement of arboviruses within and between these regions.

What is the uncertainty principle of non-relativistic quantum mechanics?

NASA Astrophysics Data System (ADS)

Riggs, Peter J.

2018-05-01

After more than ninety years of discussions over the uncertainty principle, there is still no universal agreement on what the principle states. The Robertson uncertainty relation (incorporating standard deviations) is given as the mathematical expression of the principle in most quantum mechanics textbooks. However, the uncertainty principle is not merely a statement of what any of the several uncertainty relations affirm. It is suggested that a better approach would be to present the uncertainty principle as a statement about the probability distributions of incompatible variables and the resulting restrictions on quantum states.

Instructional television utilization in the United States

NASA Technical Reports Server (NTRS)

Dumolin, J. R.

1971-01-01

Various aspects of utilizing instructional television (ITV) are summarized and evaluated and basic guidelines for future utilization of television as an instructional medium in education are considered. The role of technology in education, capabilities and limitations of television as an instructional media system and the state of ITV research efforts are discussed. Examples of various ongoing ITV programs are given and summarized. The problems involved in the three stages of the ITV process (production, distribution, and classroom utilization) are presented. A summary analysis outlines probable trends in future utilization.

Density matrix approach to the hot-electron stimulated photodesorption

NASA Astrophysics Data System (ADS)

Kühn, Oliver; May, Volkhard

1996-07-01

The dissipative dynamics of the laser-induced nonthermal desorption of small molecules from a metal surface is investigated here. Based on the density matrix formalism a multi-state model is introduced which explicitly takes into account the continuum of electronic states in the metal. Various relaxation mechanisms for the electronic degrees of freedom are shown to govern the desorption dynamics and hence the desorption probability. Particular attention is paid to the modeling of the time dependence of the electron energy distribution in the metal which reflects different excitation conditions.

Stochastic ontogenetic growth model

NASA Astrophysics Data System (ADS)

West, B. J.; West, D.

2012-02-01

An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

Modeling the probability distribution of peak discharge for infiltrating hillslopes

NASA Astrophysics Data System (ADS)

Baiamonte, Giorgio; Singh, Vijay P.

2017-07-01

Hillslope response plays a fundamental role in the prediction of peak discharge at the basin outlet. The peak discharge for the critical duration of rainfall and its probability distribution are needed for designing urban infrastructure facilities. This study derives the probability distribution, denoted as GABS model, by coupling three models: (1) the Green-Ampt model for computing infiltration, (2) the kinematic wave model for computing discharge hydrograph from the hillslope, and (3) the intensity-duration-frequency (IDF) model for computing design rainfall intensity. The Hortonian mechanism for runoff generation is employed for computing the surface runoff hydrograph. Since the antecedent soil moisture condition (ASMC) significantly affects the rate of infiltration, its effect on the probability distribution of peak discharge is investigated. Application to a watershed in Sicily, Italy, shows that with the increase of probability, the expected effect of ASMC to increase the maximum discharge diminishes. Only for low values of probability, the critical duration of rainfall is influenced by ASMC, whereas its effect on the peak discharge seems to be less for any probability. For a set of parameters, the derived probability distribution of peak discharge seems to be fitted by the gamma distribution well. Finally, an application to a small watershed, with the aim to test the possibility to arrange in advance the rational runoff coefficient tables to be used for the rational method, and a comparison between peak discharges obtained by the GABS model with those measured in an experimental flume for a loamy-sand soil were carried out.

Distributed Optimization

NASA Technical Reports Server (NTRS)

Macready, William; Wolpert, David

2005-01-01

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

Robotic Mars Sample Return: Risk Assessment and Analysis Report

NASA Technical Reports Server (NTRS)

Lalk, Thomas R.; Spence, Cliff A.

2003-01-01

A comparison of the risk associated with two alternative scenarios for a robotic Mars sample return mission was conducted. Two alternative mission scenarios were identified, the Jet Propulsion Lab (JPL) reference Mission and a mission proposed by Johnson Space Center (JSC). The JPL mission was characterized by two landers and an orbiter, and a Mars orbit rendezvous to retrieve the samples. The JSC mission (Direct/SEP) involves a solar electric propulsion (SEP) return to earth followed by a rendezvous with the space shuttle in earth orbit. A qualitative risk assessment to identify and characterize the risks, and a risk analysis to quantify the risks were conducted on these missions. Technical descriptions of the competing scenarios were developed in conjunction with NASA engineers and the sequence of events for each candidate mission was developed. Risk distributions associated with individual and combinations of events were consolidated using event tree analysis in conjunction with Monte Carlo techniques to develop probabilities of mission success for each of the various alternatives. The results were the probability of success of various end states for each candidate scenario. These end states ranged from complete success through various levels of partial success to complete failure. Overall probability of success for the Direct/SEP mission was determined to be 66% for the return of at least one sample and 58% for the JPL mission for the return of at least one sample cache. Values were also determined for intermediate events and end states as well as for the probability of violation of planetary protection. Overall mission planetary protection event probabilities of occurrence were determined to be 0.002% and 1.3% for the Direct/SEP and JPL Reference missions respectively.

Coulomb and nuclear excitations of narrow resonances in 17Ne

DOE PAGES

Marganiec, J.; Wamers, F.; Aksouh, F.; ...

2016-05-25

New experimental data for dissociation of relativistic 17Ne projectiles incident on targets of lead, carbon, and polyethylene targets at GSI are presented. Special attention is paid to the excitation and decay of narrow resonant states in 17Ne. Distributions of internal energy in the 15O+p +p three-body system have been determined together with angular and partial-energy correlations between the decay products in different energy regions. The analysis was done using existing experimental data on 17Ne and its mirror nucleus 17N. The isobaric multiplet mass equation is used for assignment of observed resonances and their spins and parities. A combination of datamore » from the heavy and light targets yielded cross sections and transition probabilities for the Coulomb excitations of the narrow resonant states. Finally, the resulting transition probabilities provide information relevant for a better understanding of the 17Ne structure.« less

Investigating Student Understanding for a Statistical Analysis of Two Thermally Interacting Solids

NASA Astrophysics Data System (ADS)

Loverude, Michael E.

2010-10-01

As part of an ongoing research and curriculum development project for upper-division courses in thermal physics, we have developed a sequence of tutorials in which students apply statistical methods to examine the behavior of two interacting Einstein solids. In the sequence, students begin with simple results from probability and develop a means for counting the states in a single Einstein solid. The students then consider the thermal interaction of two solids, and observe that the classical equilibrium state corresponds to the most probable distribution of energy between the two solids. As part of the development of the tutorial sequence, we have developed several assessment questions to probe student understanding of various aspects of this system. In this paper, we describe the strengths and weaknesses of student reasoning, both qualitative and quantitative, to assess the readiness of students for one tutorial in the sequence.

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

PubMed Central

Irvine, L A; Jafri, M S; Winslow, R L

1999-01-01

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening. PMID:10096885

Spectral Analysis of Two Coupled Diatomic Rotor Molecules

PubMed Central

Crogman, Horace T.; Harter, William G.

2014-01-01

In a previous article the theory of frame transformation relation between Body Oriented Angular (BOA) states and Lab Weakly Coupled states (LWC) was developed to investigate simple rotor–rotor interactions. By analyzing the quantum spectrum for two coupled diatomic molecules and comparing it with spectrum and probability distribution of simple models, evidence was found that, as we move from a LWC state to a strongly coupled state, a single rotor emerges in the strong limit. In the low coupling, the spectrum was quadratic which indicates the degree of floppiness in the rotor–rotor system. However in the high coupling behavior it was found that the spectrum was linear which corresponds to a rotor deep in a well. PMID:25353181

Constructing inverse probability weights for continuous exposures: a comparison of methods.

PubMed

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

Photofragment Coincidence Imaging of Small I- (H2O)n Clusters Excited to the Charge-transfer-to-solvent State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neumark, D. E. Szpunar, K. E. Kautzman, A. E. Faulhaber, and D. M.; Kautzman, K.E.; Faulhaber, A.E.

2005-11-09

The photodissociation dynamics of small I{sup -}(H{sub 2}O){sub n} (n = 2-5) clusters excited to their charge-transfer-to-solvent (CTTS) states have been studied using photofragment coincidence imaging. Upon excitation to the CTTS state, two photodissociation channels were observed. The major channel ({approx}90%) is a 2-body process forming neutral I + (H{sub 2}O){sub n} photofragments, and the minor channel is a 3-body process forming I + (H{sub 2}O){sub n-1} + H{sub 2}O fragments. Both process display translational energy (P(E{sub T})) distributions peaking at E{sub T} = 0 with little available energy partitioned into translation. Clusters excited to the detachment continuum rather thanmore » to the CTTS state display the same two channels with similar P(E{sub T}) distributions. The observation of similar P(E{sub T}) distributions from the two sets of experiments suggests that in the CTTS experiments, I atom loss occurs after autodetachment of the excited (I(H{sub 2}O){sub n}{sup -})* cluster, or, less probably, that the presence of the excess electron has little effect on the departing I atom.« less

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

Sub-poissonian photon statistics in the coherent state Jaynes-Cummings model in non-resonance

NASA Astrophysics Data System (ADS)

Zhang, Jia-tai; Fan, An-fu

1992-03-01

We study a model with a two-level atom (TLA) non-resonance interacting with a single-mode quantized cavity field (QCF). The photon number probability function, the mean photon number and Mandel's fluctuation parameter are calculated. The sub-Poissonian distributions of the photon statistics are obtained in non-resonance interaction. This statistical properties are strongly dependent on the detuning parameters.

Daily tornado frequency distributions in the United States

NASA Astrophysics Data System (ADS)

Elsner, J. B.; Jagger, T. H.; Widen, H. M.; Chavas, D. R.

2014-01-01

The authors examine daily tornado counts in the United States over the period 1994-2012 and find strong evidence for a power-law relationship in the distribution frequency. The scaling exponent is estimated at 1.64 (0.019 s.e.) giving a per tornado-day probability of 0.014% (return period of 71 years) that a tornado day produces 145 tornadoes as was observed on 27 April 2011. They also find that the total number of tornadoes by damage category on days with at least one violent tornado follows an exponential rule. On average, the daily number of tornadoes in the next lowest damage category is approximately twice the number in the current category. These findings are important and timely for tornado hazard models and for seasonal and sub-seasonal forecasts of tornado activity.

Combined risk assessment of nonstationary monthly water quality based on Markov chain and time-varying copula.

PubMed

Shi, Wei; Xia, Jun

2017-02-01

Water quality risk management is a global hot research linkage with the sustainable water resource development. Ammonium nitrogen (NH 3 -N) and permanganate index (COD Mn ) as the focus indicators in Huai River Basin, are selected to reveal their joint transition laws based on Markov theory. The time-varying moments model with either time or land cover index as explanatory variables is applied to build the time-varying marginal distributions of water quality time series. Time-varying copula model, which takes the non-stationarity in the marginal distribution and/or the time variation in dependence structure between water quality series into consideration, is constructed to describe a bivariate frequency analysis for NH 3 -N and COD Mn series at the same monitoring gauge. The larger first-order Markov joint transition probability indicates water quality state Class V w , Class IV and Class III will occur easily in the water body of Bengbu Sluice. Both marginal distribution and copula models are nonstationary, and the explanatory variable time yields better performance than land cover index in describing the non-stationarities in the marginal distributions. In modelling the dependence structure changes, time-varying copula has a better fitting performance than the copula with the constant or the time-trend dependence parameter. The largest synchronous encounter risk probability of NH 3 -N and COD Mn simultaneously reaching Class V is 50.61%, while the asynchronous encounter risk probability is largest when NH 3 -N and COD Mn is inferior to class V and class IV water quality standards, respectively.

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

NASA Technical Reports Server (NTRS)

Cohen, A. C.

1971-01-01

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

Fluctuation of the electronic coupling in DNA: Multistate versus two-state model

NASA Astrophysics Data System (ADS)

Voityuk, Alexander A.

2007-05-01

The electronic coupling for hole transfer between guanine bases G in the DNA duplex (GT) 6GTG(TG) 6 is studied using a QM/MD approach. The coupling V is calculated for 10 thousand snapshots within the two- and multistate state Generalized Mulliken-Hush model. We find that the two-state scheme considerably underestimates the rate of the hole transfer within the π stack. Moreover, the probability distributions computed with the two- and multistate schemes are quite different. It has been found that large fluctuations of V2, which are at least an order of magnitude larger than its average value, occur roughly every 1 ps.

Ignition probability of polymer-bonded explosives accounting for multiple sources of material stochasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, S.; Barua, A.; Zhou, M., E-mail: min.zhou@me.gatech.edu

2014-05-07

Accounting for the combined effect of multiple sources of stochasticity in material attributes, we develop an approach that computationally predicts the probability of ignition of polymer-bonded explosives (PBXs) under impact loading. The probabilistic nature of the specific ignition processes is assumed to arise from two sources of stochasticity. The first source involves random variations in material microstructural morphology; the second source involves random fluctuations in grain-binder interfacial bonding strength. The effect of the first source of stochasticity is analyzed with multiple sets of statistically similar microstructures and constant interfacial bonding strength. Subsequently, each of the microstructures in the multiple setsmore » is assigned multiple instantiations of randomly varying grain-binder interfacial strengths to analyze the effect of the second source of stochasticity. Critical hotspot size-temperature states reaching the threshold for ignition are calculated through finite element simulations that explicitly account for microstructure and bulk and interfacial dissipation to quantify the time to criticality (t{sub c}) of individual samples, allowing the probability distribution of the time to criticality that results from each source of stochastic variation for a material to be analyzed. Two probability superposition models are considered to combine the effects of the multiple sources of stochasticity. The first is a parallel and series combination model, and the second is a nested probability function model. Results show that the nested Weibull distribution provides an accurate description of the combined ignition probability. The approach developed here represents a general framework for analyzing the stochasticity in the material behavior that arises out of multiple types of uncertainty associated with the structure, design, synthesis and processing of materials.« less

The impacts of precipitation amount simulation on hydrological modeling in Nordic watersheds

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

Stochastic modeling of daily precipitation is very important for hydrological modeling, especially when no observed data are available. Precipitation is usually modeled by two component model: occurrence generation and amount simulation. For occurrence simulation, the most common method is the first-order two-state Markov chain due to its simplification and good performance. However, various probability distributions have been reported to simulate precipitation amount, and spatiotemporal differences exist in the applicability of different distribution models. Therefore, assessing the applicability of different distribution models is necessary in order to provide more accurate precipitation information. Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential, and hybrid exponential/Pareto distributions) are directly and indirectly evaluated on their ability to reproduce the original observed time series of precipitation amount. Data from 24 weather stations and two watersheds (Chute-du-Diable and Yamaska watersheds) in the province of Quebec (Canada) are used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three-parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear-cut when the simulated time series are used to drive a hydrological model. While the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modeling. The implications of choosing a distribution function with respect to hydrological modeling and climate change impact studies are also discussed.

Open Quantum Walks with Noncommuting Jump Operators

NASA Astrophysics Data System (ADS)

Caballar, Roland Cristopher; Petruccione, Francesco; Sinayskiy, Ilya

2014-03-01

We examine homogeneous open quantum walks along a line, wherein each forward step is due to one quantum jump operator, and each backward step due to another quantum jump operator. We assume that these two quantum jump operators do not commute with each other. We show that if the system has N internal degrees of freedom, for particular forms of these quantum jump operators, we can obtain exact probability distributions which fall into two distinct classes, namely Gaussian distributions and solitonic distributions. We also show that it is possible for a maximum of 2 solitonic distributions to be present simultaneously in the system. Finally, we consider applications of these classes of jump operators in quantum state preparation and quantum information. We acknowledge support from the National Institute for Theoretical Physics (NITheP).

Hidden regularity and universal classification of fast side chain motions in proteins

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajeshwar, Rajitha; Smith, Jeremy C.; Krishnam, Marimuthu

Proteins display characteristic dynamical signatures that appear to be universal across all proteins regardless of topology and size. Here, we systematically characterize the universal features of fast side chain motions in proteins by examining the conformational energy surfaces of individual residues obtained using enhanced sampling molecular dynamics simulation (618 free energy surfaces obtained from 0.94 s MD simulation). The side chain conformational free energy surfaces obtained using the adaptive biasing force (ABF) method for a set of eight proteins with different molecular weights and secondary structures are used to determine the methyl axial NMR order parameters (O axis 2), populationsmore » of side chain rotamer states (ρ), conformational entropies (S conf), probability fluxes, and activation energies for side chain inter-rotameric transitions. The free energy barriers separating side chain rotamer states range from 0.3 to 12 kcal/mol in all proteins and follow a trimodal distribution with an intense peak at ~5 kcal/mol and two shoulders at ~3 and ~7.5 kcal/mol, indicating that some barriers are more favored than others by proteins to maintain a balance between their conformational stability and flexibility. The origin and the influences of the trimodal barrier distribution on the distribution of O axis 2 and the side chain conformational entropy are discussed. A hierarchical grading of rotamer states based on the conformational free energy barriers, entropy, and probability flux reveals three distinct classes of side chains in proteins. A unique nonlinear correlation is established between O axis 2 and the side chain rotamer populations (ρ). In conclusion, the apparent universality in O axis 2 versus correlation, trimodal barrier distribution, and distinct characteristics of three classes of side chains observed among all proteins indicates a hidden regularity (or commonality) in the dynamical heterogeneity of fast side chain motions in proteins.« less

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

NASA Astrophysics Data System (ADS)

Lozovatsky, I.; Fernando, H. J. S.; Planella-Morato, J.; Liu, Zhiyu; Lee, J.-H.; Jinadasa, S. U. P.

2017-10-01

The probability distribution of turbulent kinetic energy dissipation rate in stratified ocean usually deviates from the classic lognormal distribution that has been formulated for and often observed in unstratified homogeneous layers of atmospheric and oceanic turbulence. Our measurements of vertical profiles of micro-scale shear, collected in the East China Sea, northern Bay of Bengal, to the south and east of Sri Lanka, and in the Gulf Stream region, show that the probability distributions of the dissipation rate ɛ˜r in the pycnoclines (r ˜ 1.4 m is the averaging scale) can be successfully modeled by the Burr (type XII) probability distribution. In weakly stratified boundary layers, lognormal distribution of ɛ˜r is preferable, although the Burr is an acceptable alternative. The skewness Skɛ and the kurtosis Kɛ of the dissipation rate appear to be well correlated in a wide range of Skɛ and Kɛ variability.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

NASA Astrophysics Data System (ADS)

Neri, Izaak; Roldán, Édgar; Jülicher, Frank

2017-01-01

We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.

ERMiT: Estimating Post-Fire Erosion in Probabilistic Terms

NASA Astrophysics Data System (ADS)

Pierson, F. B.; Robichaud, P. R.; Elliot, W. J.; Hall, D. E.; Moffet, C. A.

2006-12-01

Mitigating the impact of post-wildfire runoff and erosion on life, property, and natural resources have cost the United States government tens of millions of dollars over the past decade. The decision of where, when, and how to apply the most effective mitigation treatments requires land managers to assess the risk of damaging runoff and erosion events occurring after a fire. The Erosion Risk Management Tool (ERMiT) is a web-based application that estimates erosion in probabilistic terms on burned and recovering forest, range, and chaparral lands. Unlike most erosion prediction models, ERMiT does not provide `average annual erosion rates;' rather, it provides a distribution of erosion rates with the likelihood of their occurrence. ERMiT combines rain event variability with spatial and temporal variabilities of hillslope burn severity, soil properties, and ground cover to estimate Water Erosion Prediction Project (WEPP) model input parameter values. Based on 20 to 40 individual WEPP runs, ERMiT produces a distribution of rain event erosion rates with a probability of occurrence for each of five post-fire years. Over the 5 years of modeled recovery, the occurrence probability of the less erodible soil parameters is increased and the occurrence probability of the more erodible soil parameters is decreased. In addition, the occurrence probabilities and the four spatial arrangements of burn severity (arrangements of overland flow elements (OFE's)), are shifted toward lower burn severity with each year of recovery. These yearly adjustments are based on field measurements made through post-fire recovery periods. ERMiT also provides rain event erosion rate distributions for hillslopes that have been treated with seeding, straw mulch, straw wattles and contour-felled log erosion barriers. Such output can help managers make erosion mitigation treatment decisions based on the probability of high sediment yields occurring, the value of resources at risk for damage, cost, and other management considerations.

Evaluation of the Three Parameter Weibull Distribution Function for Predicting Fracture Probability in Composite Materials

DTIC Science & Technology

1978-03-01

for the risk of rupture for a unidirectionally laminat - ed composite subjected to pure bending. (5D This equation can be simplified further by use of...C EVALUATION OF THE THREE PARAMETER WEIBULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS. THESIS / AFIT/GAE...EVALUATION OF THE THREE PARAMETER WE1BULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS THESIS Presented

Using Geothermal Play Types as an Analogue for Estimating Potential Resource Size

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terry, Rachel; Young, Katherine

Blind geothermal systems are becoming increasingly common as more geothermal fields are developed. Geothermal development is known to have high risk in the early stages of a project development because reservoir characteristics are relatively unknown until wells are drilled. Play types (or occurrence models) categorize potential geothermal fields into groups based on geologic characteristics. To aid in lowering exploration risk, these groups' reservoir characteristics can be used as analogues in new site exploration. The play type schemes used in this paper were Moeck and Beardsmore play types (Moeck et al. 2014) and Brophy occurrence models (Brophy et al. 2011). Operatingmore » geothermal fields throughout the world were classified based on their associated play type, and then reservoir characteristics data were catalogued. The distributions of these characteristics were plotted in histograms to develop probability density functions for each individual characteristic. The probability density functions can be used as input analogues in Monte Carlo estimations of resource potential for similar play types in early exploration phases. A spreadsheet model was created to estimate resource potential in undeveloped fields. The user can choose to input their own values for each reservoir characteristic or choose to use the probability distribution functions provided from the selected play type. This paper also addresses the United States Geological Survey's 1978 and 2008 assessment of geothermal resources by comparing their estimated values to reported values from post-site development. Information from the collected data was used in the comparison for thirty developed sites in the United States. No significant trends or suggestions for methodologies could be made by the comparison.« less

Maximum caliber inference of nonequilibrium processes

NASA Astrophysics Data System (ADS)

Otten, Moritz; Stock, Gerhard

2010-07-01

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

Rare events in networks with internal and external noise

NASA Astrophysics Data System (ADS)

Hindes, J.; Schwartz, I. B.

2017-12-01

We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and time scale of rare events are considered in detail for extinction in the Susceptible-Infected-Susceptible model as an illustration. We find that when both types of noise are present, there is a crossover region as the network size is increased, where the probability exponent for large deviations no longer increases linearly with the network size. We demonstrate that the form of the crossover depends on whether the endemic state is localized near the epidemic threshold or not.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Informing disease models with temporal and spatial contact structure among GPS-collared individuals in wild populations.

PubMed

Williams, David M; Dechen Quinn, Amy C; Porter, William F

2014-01-01

Contacts between hosts are essential for transmission of many infectious agents. Understanding how contacts, and thus transmission rates, occur in space and time is critical to effectively responding to disease outbreaks in free-ranging animal populations. Contacts between animals in the wild are often difficult to observe or measure directly. Instead, one must infer contacts from metrics such as proximity in space and time. Our objective was to examine how contacts between white-tailed deer (Odocoileus virginianus) vary in space and among seasons. We used GPS movement data from 71 deer in central New York State to quantify potential direct contacts between deer and indirect overlap in space use across time and space. Daily probabilities of direct contact decreased from winter (0.05-0.14), to low levels post-parturition through summer (0.00-0.02), and increased during the rut to winter levels. The cumulative distribution for the spatial structure of direct and indirect contact probabilities around a hypothetical point of occurrence increased rapidly with distance for deer pairs separated by 1,000 m-7,000 m. Ninety-five percent of the probabilities of direct contact occurred among deer pairs within 8,500 m of one another, and 99% within 10,900 m. Probabilities of indirect contact accumulated across greater spatial extents: 95% at 11,900 m and 99% at 49,000 m. Contacts were spatially consistent across seasons, indicating that although contact rates differ seasonally, they occur proportionally across similar landscape extents. Distributions of contact probabilities across space can inform management decisions for assessing risk and allocating resources in response.

Bivariate extreme value distributions

NASA Technical Reports Server (NTRS)

Elshamy, M.

1992-01-01

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Estimation of State Transition Probabilities: A Neural Network Model

NASA Astrophysics Data System (ADS)

Saito, Hiroshi; Takiyama, Ken; Okada, Masato

2015-12-01

Humans and animals can predict future states on the basis of acquired knowledge. This prediction of the state transition is important for choosing the best action, and the prediction is only possible if the state transition probability has already been learned. However, how our brains learn the state transition probability is unknown. Here, we propose a simple algorithm for estimating the state transition probability by utilizing the state prediction error. We analytically and numerically confirmed that our algorithm is able to learn the probability completely with an appropriate learning rate. Furthermore, our learning rule reproduced experimentally reported psychometric functions and neural activities in the lateral intraparietal area in a decision-making task. Thus, our algorithm might describe the manner in which our brains learn state transition probabilities and predict future states.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

PubMed

Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

2016-05-13

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

Eruption probabilities for the Lassen Volcanic Center and regional volcanism, northern California, and probabilities for large explosive eruptions in the Cascade Range

USGS Publications Warehouse

Nathenson, Manuel; Clynne, Michael A.; Muffler, L.J. Patrick

2012-01-01

Chronologies for eruptive activity of the Lassen Volcanic Center and for eruptions from the regional mafic vents in the surrounding area of the Lassen segment of the Cascade Range are here used to estimate probabilities of future eruptions. For the regional mafic volcanism, the ages of many vents are known only within broad ranges, and two models are developed that should bracket the actual eruptive ages. These chronologies are used with exponential, Weibull, and mixed-exponential probability distributions to match the data for time intervals between eruptions. For the Lassen Volcanic Center, the probability of an eruption in the next year is 1.4x10-4 for the exponential distribution and 2.3x10-4 for the mixed exponential distribution. For the regional mafic vents, the exponential distribution gives a probability of an eruption in the next year of 6.5x10-4, but the mixed exponential distribution indicates that the current probability, 12,000 years after the last event, could be significantly lower. For the exponential distribution, the highest probability is for an eruption from a regional mafic vent. Data on areas and volumes of lava flows and domes of the Lassen Volcanic Center and of eruptions from the regional mafic vents provide constraints on the probable sizes of future eruptions. Probabilities of lava-flow coverage are similar for the Lassen Volcanic Center and for regional mafic vents, whereas the probable eruptive volumes for the mafic vents are generally smaller. Data have been compiled for large explosive eruptions (>≈ 5 km3 in deposit volume) in the Cascade Range during the past 1.2 m.y. in order to estimate probabilities of eruption. For erupted volumes >≈5 km3, the rate of occurrence since 13.6 ka is much higher than for the entire period, and we use these data to calculate the annual probability of a large eruption at 4.6x10-4. For erupted volumes ≥10 km3, the rate of occurrence has been reasonably constant from 630 ka to the present, giving more confidence in the estimate, and we use those data to calculate the annual probability of a large eruption in the next year at 1.4x10-5.

Sensitivity Analysis of the Bone Fracture Risk Model

NASA Technical Reports Server (NTRS)

Lewandowski, Beth; Myers, Jerry; Sibonga, Jean Diane

2017-01-01

Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

Modular neuron-based body estimation: maintaining consistency over different limbs, modalities, and frames of reference

PubMed Central

Ehrenfeld, Stephan; Herbort, Oliver; Butz, Martin V.

2013-01-01

This paper addresses the question of how the brain maintains a probabilistic body state estimate over time from a modeling perspective. The neural Modular Modality Frame (nMMF) model simulates such a body state estimation process by continuously integrating redundant, multimodal body state information sources. The body state estimate itself is distributed over separate, but bidirectionally interacting modules. nMMF compares the incoming sensory and present body state information across the interacting modules and fuses the information sources accordingly. At the same time, nMMF enforces body state estimation consistency across the modules. nMMF is able to detect conflicting sensory information and to consequently decrease the influence of implausible sensor sources on the fly. In contrast to the previously published Modular Modality Frame (MMF) model, nMMF offers a biologically plausible neural implementation based on distributed, probabilistic population codes. Besides its neural plausibility, the neural encoding has the advantage of enabling (a) additional probabilistic information flow across the separate body state estimation modules and (b) the representation of arbitrary probability distributions of a body state. The results show that the neural estimates can detect and decrease the impact of false sensory information, can propagate conflicting information across modules, and can improve overall estimation accuracy due to additional module interactions. Even bodily illusions, such as the rubber hand illusion, can be simulated with nMMF. We conclude with an outlook on the potential of modeling human data and of invoking goal-directed behavioral control. PMID:24191151

Predicting the ocurrence probability of freak waves baed on buoy data and non-stationary extreme value models

NASA Astrophysics Data System (ADS)

Tomas, A.; Menendez, M.; Mendez, F. J.; Coco, G.; Losada, I. J.

2012-04-01

In the last decades, freak or rogue waves have become an important topic in engineering and science. Forecasting the occurrence probability of freak waves is a challenge for oceanographers, engineers, physicists and statisticians. There are several mechanisms responsible for the formation of freak waves, and different theoretical formulations (primarily based on numerical models with simplifying assumption) have been proposed to predict the occurrence probability of freak wave in a sea state as a function of N (number of individual waves) and kurtosis (k). On the other hand, different attempts to parameterize k as a function of spectral parameters such as the Benjamin-Feir Index (BFI) and the directional spreading (Mori et al., 2011) have been proposed. The objective of this work is twofold: (1) develop a statistical model to describe the uncertainty of maxima individual wave height, Hmax, considering N and k as covariates; (2) obtain a predictive formulation to estimate k as a function of aggregated sea state spectral parameters. For both purposes, we use free surface measurements (more than 300,000 20-minutes sea states) from the Spanish deep water buoy network (Puertos del Estado, Spanish Ministry of Public Works). Non-stationary extreme value models are nowadays widely used to analyze the time-dependent or directional-dependent behavior of extreme values of geophysical variables such as significant wave height (Izaguirre et al., 2010). In this work, a Generalized Extreme Value (GEV) statistical model for the dimensionless maximum wave height (x=Hmax/Hs) in every sea state is used to assess the probability of freak waves. We allow the location, scale and shape parameters of the GEV distribution to vary as a function of k and N. The kurtosis-dependency is parameterized using third-order polynomials and the model is fitted using standard log-likelihood theory, obtaining a very good behavior to predict the occurrence probability of freak waves (x>2). Regarding the second objective of this work, we apply different algorithms using three spectral parameters (wave steepness, directional dispersion, frequential dispersion) as predictors, to estimate the probability density function of the kurtosis for a given sea state. ACKNOWLEDGMENTS The authors thank to Puertos del Estado (Spanish Ministry of Public Works) for providing the free surface measurement database.

Assessing Gaussian Assumption of PMU Measurement Error Using Field Data

DOE PAGES

Wang, Shaobu; Zhao, Junbo; Huang, Zhenyu; ...

2017-10-13

Gaussian PMU measurement error has been assumed for many power system applications, such as state estimation, oscillatory modes monitoring, voltage stability analysis, to cite a few. This letter proposes a simple yet effective approach to assess this assumption by using the stability property of a probability distribution and the concept of redundant measurement. Extensive results using field PMU data from WECC system reveal that the Gaussian assumption is questionable.

Entropy and wigner functions

PubMed

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Superconducting surface impedance under radiofrequency field

DOE PAGES

Xiao, Binping P.; Reece, Charles E.; Kelley, Michael J.

2013-04-26

Based on BCS theory with moving Cooper pairs, the electron states distribution at 0K and the probability of electron occupation with finite temperature have been derived and applied to anomalous skin effect theory to obtain the surface impedance of a superconductor under radiofrequency (RF) field. We present the numerical results for Nb and compare these with representative RF field-dependent effective surface resistance measurements from a 1.5 GHz resonant structure.

The United States, the South Atlantic, and Antarctic: Interests and Challenges

DTIC Science & Technology

1990-06-01

3) Probability of attack from the South was greatest in 1962. Not since the Navy’s 4th Fleet was based in northern Brazil during the Second World...Brazil’s attack aircraft are not carrier-borne. Brazil possesses a well-developed military armaments industry like Argentina, but its export sector far...release; ,. DECLASSIFICATIONJDOWNGRADING SCHEDULE distribution is unlimited PERFORMING ORGANIZATION REPORT NUMBER( S ) 5. MONITORING ORGANIZATION REPORT

Exact and Approximate Probabilistic Symbolic Execution

NASA Technical Reports Server (NTRS)

Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem

2014-01-01

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Statistical Inference in Hidden Markov Models Using k-Segment Constraints

PubMed Central

Titsias, Michalis K.; Holmes, Christopher C.; Yau, Christopher

2016-01-01

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. PMID:27226674

Work statistics of charged noninteracting fermions in slowly changing magnetic fields.

PubMed

Yi, Juyeon; Talkner, Peter

2011-04-01

We consider N fermionic particles in a harmonic trap initially prepared in a thermal equilibrium state at temperature β^{-1} and examine the probability density function (pdf) of the work done by a magnetic field slowly varying in time. The behavior of the pdf crucially depends on the number of particles N but also on the temperature. At high temperatures (β≪1) the pdf is given by an asymmetric Laplace distribution for a single particle, and for many particles it approaches a Gaussian distribution with variance proportional to N/β(2). At low temperatures the pdf becomes strongly peaked at the center with a variance that still linearly increases with N but exponentially decreases with the temperature. We point out the consequences of these findings for the experimental confirmation of the Jarzynski equality such as the low probability issue at high temperatures and its solution at low temperatures, together with a discussion of the crossover behavior between the two temperature regimes. ©2011 American Physical Society

Work statistics of charged noninteracting fermions in slowly changing magnetic fields

NASA Astrophysics Data System (ADS)

Yi, Juyeon; Talkner, Peter

2011-04-01

We consider N fermionic particles in a harmonic trap initially prepared in a thermal equilibrium state at temperature β-1 and examine the probability density function (pdf) of the work done by a magnetic field slowly varying in time. The behavior of the pdf crucially depends on the number of particles N but also on the temperature. At high temperatures (β≪1) the pdf is given by an asymmetric Laplace distribution for a single particle, and for many particles it approaches a Gaussian distribution with variance proportional to N/β2. At low temperatures the pdf becomes strongly peaked at the center with a variance that still linearly increases with N but exponentially decreases with the temperature. We point out the consequences of these findings for the experimental confirmation of the Jarzynski equality such as the low probability issue at high temperatures and its solution at low temperatures, together with a discussion of the crossover behavior between the two temperature regimes.

Nonparametric Density Estimation Based on Self-Organizing Incremental Neural Network for Large Noisy Data.

PubMed

Nakamura, Yoshihiro; Hasegawa, Osamu

2017-01-01

With the ongoing development and expansion of communication networks and sensors, massive amounts of data are continuously generated in real time from real environments. Beforehand, prediction of a distribution underlying such data is difficult; furthermore, the data include substantial amounts of noise. These factors make it difficult to estimate probability densities. To handle these issues and massive amounts of data, we propose a nonparametric density estimator that rapidly learns data online and has high robustness. Our approach is an extension of both kernel density estimation (KDE) and a self-organizing incremental neural network (SOINN); therefore, we call our approach KDESOINN. An SOINN provides a clustering method that learns about the given data as networks of prototype of data; more specifically, an SOINN can learn the distribution underlying the given data. Using this information, KDESOINN estimates the probability density function. The results of our experiments show that KDESOINN outperforms or achieves performance comparable to the current state-of-the-art approaches in terms of robustness, learning time, and accuracy.

Automated classification of mouse pup isolation syllables: from cluster analysis to an Excel-based "mouse pup syllable classification calculator".

PubMed

Grimsley, Jasmine M S; Gadziola, Marie A; Wenstrup, Jeffrey J

2012-01-01

Mouse pups vocalize at high rates when they are cold or isolated from the nest. The proportions of each syllable type produced carry information about disease state and are being used as behavioral markers for the internal state of animals. Manual classifications of these vocalizations identified 10 syllable types based on their spectro-temporal features. However, manual classification of mouse syllables is time consuming and vulnerable to experimenter bias. This study uses an automated cluster analysis to identify acoustically distinct syllable types produced by CBA/CaJ mouse pups, and then compares the results to prior manual classification methods. The cluster analysis identified two syllable types, based on their frequency bands, that have continuous frequency-time structure, and two syllable types featuring abrupt frequency transitions. Although cluster analysis computed fewer syllable types than manual classification, the clusters represented well the probability distributions of the acoustic features within syllables. These probability distributions indicate that some of the manually classified syllable types are not statistically distinct. The characteristics of the four classified clusters were used to generate a Microsoft Excel-based mouse syllable classifier that rapidly categorizes syllables, with over a 90% match, into the syllable types determined by cluster analysis.

Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

NASA Astrophysics Data System (ADS)

Kocia, Lucas; Love, Peter

2017-12-01

We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

On the occurrence of Cebus flavius (Schreber 1774) in the Caatinga, and the use of semi-arid environments by Cebus species in the Brazilian state of Rio Grande do Norte.

PubMed

Ferreira, Renata G; Jerusalinsky, Leandro; Silva, Thiago César Farias; de Souza Fialho, Marcos; de Araújo Roque, Alan; Fernandes, Adalberto; Arruda, Fátima

2009-10-01

Cebus flavius is a recently rediscovered species and a candidate for the 25 most endangered primate species list. It was hypothesized that the distribution of C. flavius was limited to the Atlantic Forest, while the occurrence of C. libidinosus in the Rio Grande do Norte (RN) Caatinga was inferred, given its occurrence in neighboring states. As a result of a survey in ten areas of the RN Caatinga, this paper reports on four Cebus populations, including the first occurrence of C. flavius in the Caatinga, and an expansion of the northwestern limits of distribution for the species. This C. flavius population may be a rare example of a process of geographic distribution retraction, and is probably the most endangered population of this species. New areas of occurrence of C. libidinosus are also described. Tool use sites were observed in association with reports of the presence of both capuchin species.

Probability distributions of the electroencephalogram envelope of preterm infants.

PubMed

Saji, Ryoya; Hirasawa, Kyoko; Ito, Masako; Kusuda, Satoshi; Konishi, Yukuo; Taga, Gentaro

2015-06-01

To determine the stationary characteristics of electroencephalogram (EEG) envelopes for prematurely born (preterm) infants and investigate the intrinsic characteristics of early brain development in preterm infants. Twenty neurologically normal sets of EEGs recorded in infants with a post-conceptional age (PCA) range of 26-44 weeks (mean 37.5 ± 5.0 weeks) were analyzed. Hilbert transform was applied to extract the envelope. We determined the suitable probability distribution of the envelope and performed a statistical analysis. It was found that (i) the probability distributions for preterm EEG envelopes were best fitted by lognormal distributions at 38 weeks PCA or less, and by gamma distributions at 44 weeks PCA; (ii) the scale parameter of the lognormal distribution had positive correlations with PCA as well as a strong negative correlation with the percentage of low-voltage activity; (iii) the shape parameter of the lognormal distribution had significant positive correlations with PCA; (iv) the statistics of mode showed significant linear relationships with PCA, and, therefore, it was considered a useful index in PCA prediction. These statistics, including the scale parameter of the lognormal distribution and the skewness and mode derived from a suitable probability distribution, may be good indexes for estimating stationary nature in developing brain activity in preterm infants. The stationary characteristics, such as discontinuity, asymmetry, and unimodality, of preterm EEGs are well indicated by the statistics estimated from the probability distribution of the preterm EEG envelopes. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

An application of the Krylov-FSP-SSA method to parameter fitting with maximum likelihood

NASA Astrophysics Data System (ADS)

Dinh, Khanh N.; Sidje, Roger B.

2017-12-01

Monte Carlo methods such as the stochastic simulation algorithm (SSA) have traditionally been employed in gene regulation problems. However, there has been increasing interest to directly obtain the probability distribution of the molecules involved by solving the chemical master equation (CME). This requires addressing the curse of dimensionality that is inherent in most gene regulation problems. The finite state projection (FSP) seeks to address the challenge and there have been variants that further reduce the size of the projection or that accelerate the resulting matrix exponential. The Krylov-FSP-SSA variant has proved numerically efficient by combining, on one hand, the SSA to adaptively drive the FSP, and on the other hand, adaptive Krylov techniques to evaluate the matrix exponential. Here we apply this Krylov-FSP-SSA to a mutual inhibitory gene network synthetically engineered in Saccharomyces cerevisiae, in which bimodality arises. We show numerically that the approach can efficiently approximate the transient probability distribution, and this has important implications for parameter fitting, where the CME has to be solved for many different parameter sets. The fitting scheme amounts to an optimization problem of finding the parameter set so that the transient probability distributions fit the observations with maximum likelihood. We compare five optimization schemes for this difficult problem, thereby providing further insights into this approach of parameter estimation that is often applied to models in systems biology where there is a need to calibrate free parameters. Work supported by NSF grant DMS-1320849.

Diversity of multilayer networks and its impact on collaborating epidemics

NASA Astrophysics Data System (ADS)

Min, Yong; Hu, Jiaren; Wang, Weihong; Ge, Ying; Chang, Jie; Jin, Xiaogang

2014-12-01

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressing (competitive interaction), or inducing (collaborating interaction) its diffusion on other layers. Collaborating interaction displays different patterns: (i) random collaboration, where intralayer or interlayer induction has the same probability; (ii) concentrating collaboration, where consecutive intralayer induction is guaranteed with a probability of 1; and (iii) cascading collaboration, where consecutive intralayer induction is banned with a probability of 0. In this paper, we develop a top-bottom framework that uses only two distributions, the overlaid degree distribution and edge-type distribution, to model collaborating epidemics on multilayer networks. We then state the response of three collaborating patterns to structural diversity (evenness and difference of network layers). For viral agents with small transmissibility, we find that random collaboration is more effective in networks with higher diversity (high evenness and difference), while the concentrating pattern is more suitable in uneven networks. Interestingly, the cascading pattern requires a network with moderate difference and high evenness, and the moderately uneven coupling of multiple network layers can effectively increase robustness to resist cascading failure. With large transmissibility, however, we find that all collaborating patterns are more effective in high-diversity networks. Our work provides a systemic analysis of collaborating epidemics on multilayer networks. The results enhance our understanding of biotic and informative diffusion through multiple vectors.

Decay channels of Al L sub 2,3 excitons and the absence of O K excitons in. alpha. -Al sub 2 O sub 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Brien, W.L.; Jia, J.; Dong, Q.

1991-12-15

The Al {ital L}{sub 2,3} and O {ital K} thresholds for single-crystal {alpha}-Al{sub 2}O{sub 3} have been studied by photoemission. Energy-distribution curves, constant-initial-state (CIS), and constant-final-state (CFS) spectra are reported and compared to the absorption spectrum reported previously. An exciton appears as a doublet at threshold in the Al {ital L}{sub 2,3} CFS, CIS, and absorption spectra. The details of the Al {ital L}{sub 2,3} CFS spectrum and absorption spectrum are similar, while the exciton is the only feature present in the CIS spectrum. Comparisons of the various Al {ital L}{sub 2,3} spectra allow the probabilities of different exciton decaymore » channels to be determined. The probability for nonradiative direct recombination of the exciton is found to be (8{plus minus}1)% and the probability for Auger decay of the exciton is found to be (72{plus minus}20)%. Comparisons of the O {ital K} CIS and CFS spectra suggest that no O {ital K} exciton is formed.« less

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Distributed Constrained Optimization with Semicoordinate Transformations

NASA Technical Reports Server (NTRS)

Macready, William; Wolpert, David

2006-01-01

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.

Agricultural pesticide use in California: pesticide prioritization, use densities, and population distributions for a childhood cancer study.

PubMed Central

Gunier, R B; Harnly, M E; Reynolds, P; Hertz, A; Von Behren, J

2001-01-01

Several studies have suggested an association between childhood cancer and pesticide exposure. California leads the nation in agricultural pesticide use. A mandatory reporting system for all agricultural pesticide use in the state provides information on the active ingredient, amount used, and location. We calculated pesticide use density to quantify agricultural pesticide use in California block groups for a childhood cancer study. Pesticides with similar toxicologic properties (probable carcinogens, possible carcinogens, genotoxic compounds, and developmental or reproductive toxicants) were grouped together for this analysis. To prioritize pesticides, we weighted pesticide use by the carcinogenic and exposure potential of each compound. The top-ranking individual pesticides were propargite, methyl bromide, and trifluralin. We used a geographic information system to calculate pesticide use density in pounds per square mile of total land area for all United States census-block groups in the state. Most block groups (77%) averaged less than 1 pound per square mile of use for 1991-1994 for pesticides classified as probable human carcinogens. However, at the high end of use density (> 90th percentile), there were 493 block groups with more than 569 pounds per square mile. Approximately 170,000 children under 15 years of age were living in these block groups in 1990. The distribution of agricultural pesticide use and number of potentially exposed children suggests that pesticide use density would be of value for a study of childhood cancer. PMID:11689348

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

NASA Astrophysics Data System (ADS)

Anastopoulos, C.; Hu, B. L.

2018-02-01

We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

[Research on engine remaining useful life prediction based on oil spectrum analysis and particle filtering].

PubMed

Sun, Lei; Jia, Yun-xian; Cai, Li-ying; Lin, Guo-yu; Zhao, Jin-song

2013-09-01

The spectrometric oil analysis(SOA) is an important technique for machine state monitoring, fault diagnosis and prognosis, and SOA based remaining useful life(RUL) prediction has an advantage of finding out the optimal maintenance strategy for machine system. Because the complexity of machine system, its health state degradation process can't be simply characterized by linear model, while particle filtering(PF) possesses obvious advantages over traditional Kalman filtering for dealing nonlinear and non-Gaussian system, the PF approach was applied to state forecasting by SOA, and the RUL prediction technique based on SOA and PF algorithm is proposed. In the prediction model, according to the estimating result of system's posterior probability, its prior probability distribution is realized, and the multi-step ahead prediction model based on PF algorithm is established. Finally, the practical SOA data of some engine was analyzed and forecasted by the above method, and the forecasting result was compared with that of traditional Kalman filtering method. The result fully shows the superiority and effectivity of the

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture.

PubMed

Campbell, Earl T; Eisert, Jens

2012-01-13

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

Effect of temperature and thermal history on borosilicate glass structure

NASA Astrophysics Data System (ADS)

Angeli, Frédéric; Villain, Olivier; Schuller, Sophie; Charpentier, Thibault; de Ligny, Dominique; Bressel, Lena; Wondraczek, Lothar

2012-02-01

The influence of the temperature and quenching rate on the structure of a borosilicate glass was studied by high-resolution solid-state 11B, 23Na, 29Si nuclear magnetic resonance (NMR) and high-temperature Raman spectroscopy. Data were obtained for glass in the solid state after annealing and quenching at cooling rates covering four orders of magnitude as well as in the liquid state from Raman experiments and from calorimetry and rheological data. Nuclear magnetic resonance measurements were used to calibrate the Raman spectra in order to quantify the change in boron coordination with temperature. This result can then be used to determine the fictive temperature of the glass directly from the boron coordination. The fictive temperature, heat capacity, and configurational entropy are extracted from calorimetry and viscosity measurements. Changes in the boron coordination account for only 25% of the configurational heat capacity of the liquid. The structural parameters capable of accounting for the remaining quantity are discussed on the basis of structural data, both local (inhomogeneity of the sodium distribution) and medium-range (from NMR parameter distribution). It has thus been shown that, although the B-O-B angular distributions of the boroxol rings (and probably the Si-O-Si distributions) are not affected by temperature, a structural disorder is identified through the angular distributions of the bonds linking borate and silicate groups.

Some Classes of Imperfect Information Finite State-Space Stochastic Games with Finite-Dimensional Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

McEneaney, William M.

2004-08-15

Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity ofmore » an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.« less

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution

PubMed Central

Dinov, Ivo D.; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2014-01-01

Summary Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students’ understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference. PMID:25419016

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution.

PubMed

Dinov, Ivo D; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2013-01-01

Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students' understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference.

Study of nonequilibrium work distributions from a fluctuating lattice Boltzmann model.

PubMed

Nasarayya Chari, S Siva; Murthy, K P N; Inguva, Ramarao

2012-04-01

A system of ideal gas is switched from an initial equilibrium state to a final state not necessarily in equilibrium, by varying a macroscopic control variable according to a well-defined protocol. The distribution of work performed during the switching process is obtained. The equilibrium free energy difference, ΔF, is determined from the work fluctuation relation. Some of the work values in the ensemble shall be less than ΔF. We term these as ones that "violate" the second law of thermodynamics. A fluctuating lattice Boltzmann model has been employed to carry out the simulation of the switching experiment. Our results show that the probability of violation of the second law increases with the increase of switching time (τ) and tends to one-half in the reversible limit of τ→∞.

Two-dimensional description of surface-bounded exospheres with application to the migration of water molecules on the Moon

NASA Astrophysics Data System (ADS)

Schorghofer, Norbert

2015-05-01

On the Moon, water molecules and other volatiles are thought to migrate along ballistic trajectories. Here, this migration process is described in terms of a two-dimensional partial differential equation for the surface concentration, based on the probability distribution of thermal ballistic hops. A random-walk model, a corresponding diffusion coefficient, and a continuum description are provided. In other words, a surface-bounded exosphere is described purely in terms of quantities on the surface, which can provide computational and conceptual advantages. The derived continuum equation can be used to calculate the steady-state distribution of the surface concentration of volatile water molecules. An analytic steady-state solution is obtained for an equatorial ring; it reveals the width and mass of the pileup of molecules at the morning terminator.

Behavioral connectivity among bighorn sheep suggests potential for disease spread

USGS Publications Warehouse

Borg, Nathan J.; Mitchell, Michael S.; Lukacs, Paul M.; Mack, Curt M.; Waits, Lisette P.; Krausman, Paul R.

2017-01-01

Connectivity is important for population persistence and can reduce the potential for inbreeding depression. Connectivity between populations can also facilitate disease transmission; respiratory diseases are one of the most important factors affecting populations of bighorn sheep (Ovis canadensis). The mechanisms of connectivity in populations of bighorn sheep likely have implications for spread of disease, but the behaviors leading to connectivity between bighorn sheep groups are not well understood. From 2007–2012, we radio-collared and monitored 56 bighorn sheep in the Salmon River canyon in central Idaho. We used cluster analysis to define social groups of bighorn sheep and then estimated connectivity between these groups using a multi-state mark-recapture model. Social groups of bighorn sheep were spatially segregated and linearly distributed along the Salmon River canyon. Monthly probabilities of movement between adjacent male and female groups ranged from 0.08 (±0.004 SE) to 0.76 (±0.068) for males and 0.05 (±0.132) to 0.24 (±0.034) for females. Movements of males were extensive and probabilities of movement were considerably higher during the rut. Probabilities of movement for females were typically smaller than those of males and did not change seasonally. Whereas adjacent groups of bighorn sheep along the Salmon River canyon were well connected, connectivity between groups north and south of the Salmon River was limited. The novel application of a multi-state model to a population of bighorn sheep allowed us to estimate the probability of movement between adjacent social groups and approximate the level of connectivity across the population. Our results suggest high movement rates of males during the rut are the most likely to result in transmission of pathogens among both male and female groups. Potential for disease spread among female groups was smaller but non-trivial. Land managers can plan grazing of domestic sheep for spring and summer months when males are relatively inactive. Removal or quarantine of social groups may reduce probability of disease transmission in populations of bighorn sheep consisting of linearly distributed social groups.

Distribution of arsenic and copper in sediment pore water: an ecological risk assessment case study for offshore drilling waste discharges.

PubMed

Sadiq, Rehan; Husain, Tahir; Veitch, Brian; Bose, Neil

2003-12-01

Due to the hydrophobic nature of synthetic based fluids (SBFs), drilling cuttings are not very dispersive in the water column and settle down close to the disposal site. Arsenic and copper are two important toxic heavy metals, among others, found in the drilling waste. In this article, the concentrations of heavy metals are determined using a steady state "aquivalence-based" fate model in a probabilistic mode. Monte Carlo simulations are employed to determine pore water concentrations. A hypothetical case study is used to determine the water quality impacts for two discharge options: 4% and 10% attached SBFs, which correspond to the best available technology option and the current discharge practice in the U.S. offshore. The exposure concentration (CE) is a predicted environmental concentration, which is adjusted for exposure probability and bioavailable fraction of heavy metals. The response of the ecosystem (RE) is defined by developing an empirical distribution function of predicted no-effect concentration. The pollutants' pore water concentrations within the radius of 750 m are estimated and cumulative distributions of risk quotient (RQ=CE/RE) are developed to determine the probability of RQ greater than 1.

Application of Probabilistic Methods for the Determination of an Economically Robust HSCT Configuration

NASA Technical Reports Server (NTRS)

Mavris, Dimitri N.; Bandte, Oliver; Schrage, Daniel P.

1996-01-01

This paper outlines an approach for the determination of economically viable robust design solutions using the High Speed Civil Transport (HSCT) as a case study. Furthermore, the paper states the advantages of a probability based aircraft design over the traditional point design approach. It also proposes a new methodology called Robust Design Simulation (RDS) which treats customer satisfaction as the ultimate design objective. RDS is based on a probabilistic approach to aerospace systems design, which views the chosen objective as a distribution function introduced by so called noise or uncertainty variables. Since the designer has no control over these variables, a variability distribution is defined for each one of them. The cumulative effect of all these distributions causes the overall variability of the objective function. For cases where the selected objective function depends heavily on these noise variables, it may be desirable to obtain a design solution that minimizes this dependence. The paper outlines a step by step approach on how to achieve such a solution for the HSCT case study and introduces an evaluation criterion which guarantees the highest customer satisfaction. This customer satisfaction is expressed by the probability of achieving objective function values less than a desired target value.

An exactly solvable coarse-grained model for species diversity

NASA Astrophysics Data System (ADS)

Suweis, Samir; Rinaldo, Andrea; Maritan, Amos

2012-07-01

We present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology.

Stylized facts in internal rates of return on stock index and its derivative transactions

NASA Astrophysics Data System (ADS)

Pichl, Lukáš; Kaizoji, Taisei; Yamano, Takuya

2007-08-01

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.

Probabilistic Reasoning for Robustness in Automated Planning

NASA Technical Reports Server (NTRS)

Schaffer, Steven; Clement, Bradley; Chien, Steve

2007-01-01

A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.

Mathematical Model to estimate the wind power using four-parameter Burr distribution

NASA Astrophysics Data System (ADS)

Liu, Sanming; Wang, Zhijie; Pan, Zhaoxu

2018-03-01

When the real probability of wind speed in the same position needs to be described, the four-parameter Burr distribution is more suitable than other distributions. This paper introduces its important properties and characteristics. Also, the application of the four-parameter Burr distribution in wind speed prediction is discussed, and the expression of probability distribution of output power of wind turbine is deduced.

Entropy Methods For Univariate Distributions in Decision Analysis

NASA Astrophysics Data System (ADS)

Abbas, Ali E.

2003-03-01

One of the most important steps in decision analysis practice is the elicitation of the decision-maker's belief about an uncertainty of interest in the form of a representative probability distribution. However, the probability elicitation process is a task that involves many cognitive and motivational biases. Alternatively, the decision-maker may provide other information about the distribution of interest, such as its moments, and the maximum entropy method can be used to obtain a full distribution subject to the given moment constraints. In practice however, decision makers cannot readily provide moments for the distribution, and are much more comfortable providing information about the fractiles of the distribution of interest or bounds on its cumulative probabilities. In this paper we present a graphical method to determine the maximum entropy distribution between upper and lower probability bounds and provide an interpretation for the shape of the maximum entropy distribution subject to fractile constraints, (FMED). We also discuss the problems with the FMED in that it is discontinuous and flat over each fractile interval. We present a heuristic approximation to a distribution if in addition to its fractiles, we also know it is continuous and work through full examples to illustrate the approach.

Scalable implementation of boson sampling with trapped ions.

PubMed

Shen, C; Zhang, Z; Duan, L-M

2014-02-07

Boson sampling solves a classically intractable problem by sampling from a probability distribution given by matrix permanents. We propose a scalable implementation of boson sampling using local transverse phonon modes of trapped ions to encode the bosons. The proposed scheme allows deterministic preparation and high-efficiency readout of the bosons in the Fock states and universal mode mixing. With the state-of-the-art trapped ion technology, it is feasible to realize boson sampling with tens of bosons by this scheme, which would outperform the most powerful classical computers and constitute an effective disproof of the famous extended Church-Turing thesis.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

NASA Astrophysics Data System (ADS)

Bhattacharjee, J. K.; Kirkpatrick, T. R.; Sengers, J. V.

2018-04-01

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Methods to elicit probability distributions from experts: a systematic review of reported practice in health technology assessment.

PubMed

Grigore, Bogdan; Peters, Jaime; Hyde, Christopher; Stein, Ken

2013-11-01

Elicitation is a technique that can be used to obtain probability distribution from experts about unknown quantities. We conducted a methodology review of reports where probability distributions had been elicited from experts to be used in model-based health technology assessments. Databases including MEDLINE, EMBASE and the CRD database were searched from inception to April 2013. Reference lists were checked and citation mapping was also used. Studies describing their approach to the elicitation of probability distributions were included. Data was abstracted on pre-defined aspects of the elicitation technique. Reports were critically appraised on their consideration of the validity, reliability and feasibility of the elicitation exercise. Fourteen articles were included. Across these studies, the most marked features were heterogeneity in elicitation approach and failure to report key aspects of the elicitation method. The most frequently used approaches to elicitation were the histogram technique and the bisection method. Only three papers explicitly considered the validity, reliability and feasibility of the elicitation exercises. Judged by the studies identified in the review, reports of expert elicitation are insufficient in detail and this impacts on the perceived usability of expert-elicited probability distributions. In this context, the wider credibility of elicitation will only be improved by better reporting and greater standardisation of approach. Until then, the advantage of eliciting probability distributions from experts may be lost.

Computer simulation of random variables and vectors with arbitrary probability distribution laws

NASA Technical Reports Server (NTRS)

Bogdan, V. M.

1981-01-01

Assume that there is given an arbitrary n-dimensional probability distribution F. A recursive construction is found for a sequence of functions x sub 1 = f sub 1 (U sub 1, ..., U sub n), ..., x sub n = f sub n (U sub 1, ..., U sub n) such that if U sub 1, ..., U sub n are independent random variables having uniform distribution over the open interval (0,1), then the joint distribution of the variables x sub 1, ..., x sub n coincides with the distribution F. Since uniform independent random variables can be well simulated by means of a computer, this result allows one to simulate arbitrary n-random variables if their joint probability distribution is known.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W., Dr.

1991-01-01

The use of a radioisotope thermoelectric generator fueled with plutonium-238 dioxide on the Space Shuttle-launched Ulysses mission implies some level of risk due to potential accidents. This paper describes the method used to quantify risks in the Ulysses mission Final Safety Analysis Report prepared for the U.S. Department of Energy. The starting point for the analysis described herein is following input of source term probability distributions from the General Electric Company. A Monte Carlo technique is used to develop probability distributions of radiological consequences for a range of accident scenarios thoughout the mission. Factors affecting radiological consequences are identified, the probability distribution of the effect of each factor determined, and the functional relationship among all the factors established. The probability distributions of all the factor effects are then combined using a Monte Carlo technique. The results of the analysis are presented in terms of complementary cumulative distribution functions (CCDF) by mission sub-phase, phase, and the overall mission. The CCDFs show the total probability that consequences (calculated health effects) would be equal to or greater than a given value.

Force Density Function Relationships in 2-D Granular Media

NASA Technical Reports Server (NTRS)

Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.

2004-01-01

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration.

PubMed

Schreiber, Christoph; Segerer, Felix J; Wagner, Ernst; Roidl, Andreas; Rädler, Joachim O

2016-05-31

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

Many frequency distributions have been used to evaluate monthly precipitation probabilities. Eight of these distributions (including Pearson type III, extreme value, and transform normal probability density functions) are comparatively examined to determine their ability to represent accurately variations in monthly precipitation totals for global hydroclimatological analyses. Results indicate that a modified version of the Box-Cox transform-normal distribution more adequately describes the 'true' precipitation distribution than does any of the other methods. This assessment was made using a cross-validation procedure for a global network of 253 stations for which at least 100 years of monthly precipitation totals were available.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jimenez, O.; Roa, Luis; Delgado, A.

We study the probabilistic cloning of equidistant states. These states are such that the inner product between them is a complex constant or its conjugate. Thereby, it is possible to study their cloning in a simple way. In particular, we are interested in the behavior of the cloning probability as a function of the phase of the overlap among the involved states. We show that for certain families of equidistant states Duan and Guo's cloning machine leads to cloning probabilities lower than the optimal unambiguous discrimination probability of equidistant states. We propose an alternative cloning machine whose cloning probability ismore » higher than or equal to the optimal unambiguous discrimination probability for any family of equidistant states. Both machines achieve the same probability for equidistant states whose inner product is a positive real number.« less

q-Gaussian distributions of leverage returns, first stopping times, and default risk valuations

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Tian, Li

2013-10-01

We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q-Gaussian distributions with the Tsallis entropic parameter within the interval 1

The orbital PDF: general inference of the gravitational potential from steady-state tracers

NASA Astrophysics Data System (ADS)

Han, Jiaxin; Wang, Wenting; Cole, Shaun; Frenk, Carlos S.

2016-02-01

We develop two general methods to infer the gravitational potential of a system using steady-state tracers, I.e. tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time independence implies a universal orbital probability density function (oPDF) dP(λ|orbit) ∝ dt, where λ is the coordinate of the particle along the orbit. The oPDF is equivalent to Jeans theorem, and is the key physical ingredient behind most dynamical modelling of steady-state tracers. In the case of a spherical potential, we develop a likelihood estimator that fits analytical potentials to the system and a non-parametric method (`phase-mark') that reconstructs the potential profile, both assuming only the oPDF. The methods involve no extra assumptions about the tracer distribution function and can be applied to tracers with any arbitrary distribution of orbits, with possible extension to non-spherical potentials. The methods are tested on Monte Carlo samples of steady-state tracers in dark matter haloes to show that they are unbiased as well as efficient. A fully documented C/PYTHON code implementing our method is freely available at a GitHub repository linked from http://icc.dur.ac.uk/data/#oPDF.

Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks

PubMed Central

Hallen, Mark; Li, Bochong; Tanouchi, Yu; Tan, Cheemeng; West, Mike; You, Lingchong

2011-01-01

Cellular processes are “noisy”. In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry. PMID:22022252

Work fluctuations for Bose particles in grand canonical initial states.

PubMed

Yi, Juyeon; Kim, Yong Woon; Talkner, Peter

2012-05-01

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall-off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.

Improved key-rate bounds for practical decoy-state quantum-key-distribution systems

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Zhao, Qi; Razavi, Mohsen; Ma, Xiongfeng

2017-01-01

The decoy-state scheme is the most widely implemented quantum-key-distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key-rate bounds obtained from these techniques and that obtained from the Gaussian assumption. Here we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our method almost closes the gap between the two previously proposed techniques and achieves a performance similar to that of conventional Gaussian approximations.

Faithful Pointer for Qubit Measurement

NASA Astrophysics Data System (ADS)

Kumari, Asmita; Pan, A. K.

2018-02-01

In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out that mutual orthogonality (formal idealness) does not necessarily imply the real space distinguishability (operational idealness), but converse is true. In fact, for the commonly referred Gaussian wavefunction, it is possible to obtain a measurement situation which is formally ideal but fully nonideal operationally. In this paper, we derive a class of pointer states, that we call faithful pointers, for which the degree of formal (non)idealness is equal to the operational (non)idealness. In other words, for the faithful pointers, if a measurement situation is formally ideal then it is operationally ideal and vice versa.

Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form

USGS Publications Warehouse

Greenwood, J. Arthur; Landwehr, J. Maciunas; Matalas, N.C.; Wallis, J.R.

1979-01-01

Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.

Univariate Probability Distributions

ERIC Educational Resources Information Center

Leemis, Lawrence M.; Luckett, Daniel J.; Powell, Austin G.; Vermeer, Peter E.

2012-01-01

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…

A probability space for quantum models

NASA Astrophysics Data System (ADS)

Lemmens, L. F.

2017-06-01

A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.

Statistics of partially-polarized fields: beyond the Stokes vector and coherence matrix

NASA Astrophysics Data System (ADS)

Charnotskii, Mikhail

2017-08-01

Traditionally, the partially-polarized light is characterized by the four Stokes parameters. Equivalent description is also provided by correlation tensor of the optical field. These statistics specify only the second moments of the complex amplitudes of the narrow-band two-dimensional electric field of the optical wave. Electric field vector of the random quasi monochromatic wave is a nonstationary oscillating two-dimensional real random variable. We introduce a novel statistical description of these partially polarized waves: the Period-Averaged Probability Density Function (PA-PDF) of the field. PA-PDF contains more information on the polarization state of the field than the Stokes vector. In particular, in addition to the conventional distinction between the polarized and depolarized components of the field PA-PDF allows to separate the coherent and fluctuating components of the field. We present several model examples of the fields with identical Stokes vectors and very distinct shapes of PA-PDF. In the simplest case of the nonstationary, oscillating normal 2-D probability distribution of the real electrical field and stationary 4-D probability distribution of the complex amplitudes, the newly-introduced PA-PDF is determined by 13 parameters that include the first moments and covariance matrix of the quadrature components of the oscillating vector field.

Correcting Classifiers for Sample Selection Bias in Two-Phase Case-Control Studies

PubMed Central

Theis, Fabian J.

2017-01-01

Epidemiological studies often utilize stratified data in which rare outcomes or exposures are artificially enriched. This design can increase precision in association tests but distorts predictions when applying classifiers on nonstratified data. Several methods correct for this so-called sample selection bias, but their performance remains unclear especially for machine learning classifiers. With an emphasis on two-phase case-control studies, we aim to assess which corrections to perform in which setting and to obtain methods suitable for machine learning techniques, especially the random forest. We propose two new resampling-based methods to resemble the original data and covariance structure: stochastic inverse-probability oversampling and parametric inverse-probability bagging. We compare all techniques for the random forest and other classifiers, both theoretically and on simulated and real data. Empirical results show that the random forest profits from only the parametric inverse-probability bagging proposed by us. For other classifiers, correction is mostly advantageous, and methods perform uniformly. We discuss consequences of inappropriate distribution assumptions and reason for different behaviors between the random forest and other classifiers. In conclusion, we provide guidance for choosing correction methods when training classifiers on biased samples. For random forests, our method outperforms state-of-the-art procedures if distribution assumptions are roughly fulfilled. We provide our implementation in the R package sambia. PMID:29312464

Regional probability distribution of the annual reference evapotranspiration and its effective parameters in Iran

NASA Astrophysics Data System (ADS)

Khanmohammadi, Neda; Rezaie, Hossein; Montaseri, Majid; Behmanesh, Javad

2017-10-01

The reference evapotranspiration (ET0) plays an important role in water management plans in arid or semi-arid countries such as Iran. For this reason, the regional analysis of this parameter is important. But, ET0 process is affected by several meteorological parameters such as wind speed, solar radiation, temperature and relative humidity. Therefore, the effect of distribution type of effective meteorological variables on ET0 distribution was analyzed. For this purpose, the regional probability distribution of the annual ET0 and its effective parameters were selected. Used data in this research was recorded data at 30 synoptic stations of Iran during 1960-2014. Using the probability plot correlation coefficient (PPCC) test and the L-moment method, five common distributions were compared and the best distribution was selected. The results of PPCC test and L-moment diagram indicated that the Pearson type III distribution was the best probability distribution for fitting annual ET0 and its four effective parameters. The results of RMSE showed that the ability of the PPCC test and L-moment method for regional analysis of reference evapotranspiration and its effective parameters was similar. The results also showed that the distribution type of the parameters which affected ET0 values can affect the distribution of reference evapotranspiration.

Probabilistic reasoning in data analysis.

PubMed

Sirovich, Lawrence

2011-09-20

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Work probability distribution and tossing a biased coin

NASA Astrophysics Data System (ADS)

Saha, Arnab; Bhattacharjee, Jayanta K.; Chakraborty, Sagar

2011-01-01

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for the Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modeling other physical phenomena where rare events play an important role.

Weighted Parzen Windows for Pattern Classification

DTIC Science & Technology

1994-05-01

Nearest-Neighbor Rule The k-Nearest-Neighbor ( kNN ) technique is nonparametric, assuming nothing about the distribution of the data. Stated succinctly...probabilities P(wj I x) from samples." Raudys and Jain [20:255] advance this interpretation by pointing out that the kNN technique can be viewed as the...34Parzen window classifier with a hyper- rectangular window function." As with the Parzen-window technique, the kNN classifier is more accurate as the

Constraining the mass and radius of neutron stars in globular clusters

NASA Astrophysics Data System (ADS)

Steiner, A. W.; Heinke, C. O.; Bogdanov, S.; Li, C. K.; Ho, W. C. G.; Bahramian, A.; Han, S.

2018-05-01

We analyse observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. The distance uncertainty is implemented in a new Gaussian blurring method that can be directly applied to the probability distribution over mass and radius. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions in the equation of state are preferred, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.

A probabilistic tornado wind hazard model for the continental United States

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hossain, Q; Kimball, J; Mensing, R

A probabilistic tornado wind hazard model for the continental United States (CONUS) is described. The model incorporates both aleatory (random) and epistemic uncertainties associated with quantifying the tornado wind hazard parameters. The temporal occurrences of tornadoes within the continental United States (CONUS) is assumed to be a Poisson process. A spatial distribution of tornado touchdown locations is developed empirically based on the observed historical events within the CONUS. The hazard model is an aerial probability model that takes into consideration the size and orientation of the facility, the length and width of the tornado damage area (idealized as a rectanglemore » and dependent on the tornado intensity scale), wind speed variation within the damage area, tornado intensity classification errors (i.e.,errors in assigning a Fujita intensity scale based on surveyed damage), and the tornado path direction. Epistemic uncertainties in describing the distributions of the aleatory variables are accounted for by using more than one distribution model to describe aleatory variations. The epistemic uncertainties are based on inputs from a panel of experts. A computer program, TORNADO, has been developed incorporating this model; features of this program are also presented.« less

Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

PubMed

Thattai, Mukund

2016-01-19

Messenger RNA (mRNA) dynamics in single cells are often modeled as a memoryless birth-death process with a constant probability per unit time that an mRNA molecule is synthesized or degraded. This predicts a Poisson steady-state distribution of mRNA number, in close agreement with experiments. This is surprising, since mRNA decay is known to be a complex process. The paradox is resolved by realizing that the Poisson steady state generalizes to arbitrary mRNA lifetime distributions. A mapping between mRNA dynamics and queueing theory highlights an identifiability problem: a measured Poisson steady state is consistent with a large variety of microscopic models. Here, I provide a rigorous and intuitive explanation for the universality of the Poisson steady state. I show that the mRNA birth-death process and its complex decay variants all take the form of the familiar Poisson law of rare events, under a nonlinear rescaling of time. As a corollary, not only steady-states but also transients are Poisson distributed. Deviations from the Poisson form occur only under two conditions, promoter fluctuations leading to transcriptional bursts or nonindependent degradation of mRNA molecules. These results place severe limits on the power of single-cell experiments to probe microscopic mechanisms, and they highlight the need for single-molecule measurements. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Hybrid computer technique yields random signal probability distributions

NASA Technical Reports Server (NTRS)

Cameron, W. D.

1965-01-01

Hybrid computer determines the probability distributions of instantaneous and peak amplitudes of random signals. This combined digital and analog computer system reduces the errors and delays of manual data analysis.

Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

NASA Astrophysics Data System (ADS)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2014 CFR

2014-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2011 CFR

2011-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

PubMed

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We recommend the use of cumulative probability to fit parametric probability distributions to propagule retention time, specifically using maximum likelihood for parameter estimation. Furthermore, the experimental design for an optimal characterization of unimodal propagule retention time should contemplate at least 500 recovered propagules and sampling time-intervals not larger than the time peak of propagule retrieval, except in the tail of the distribution where broader sampling time-intervals may also produce accurate fits.

How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

ERIC Educational Resources Information Center

Derouet, Charlotte; Parzysz, Bernard

2016-01-01

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

Multiple product pathways in photodissociation of nitromethane at 213 nm

NASA Astrophysics Data System (ADS)

Sumida, Masataka; Kohge, Yasunori; Yamasaki, Katsuyoshi; Kohguchi, Hiroshi

2016-02-01

In this paper, we present a photodissociation dynamics study of nitromethane at 213 nm in the π → π* transition. Resonantly enhanced multiphoton ionization spectroscopy and ion-imaging were applied to measure the internal state distributions and state-resolved scattering distributions of the CH3, NO(X 2Π, A 2Σ+), and O(3PJ) photofragments. The rotationally state-resolved scattering distribution of the CH3 fragment showed two velocity components, of which the slower one decreased the relative intensity as the rotational and vibrational excitations. The translational energy distribution of the faster CH3 fragment indicated the production of the NO2 counter-product in the electronic excited state, wherein 1 2B2 was the most probable. The NO(v = 0) fragment exhibited a bimodal translational energy distribution, whereas the NO(v = 1 and 2) fragment exhibited a single translational energy component with a relatively larger internal energy. The translational energy of a portion of the O(3PJ) photofragment was found to be higher than the one-photon dissociation threshold, indicating the two-photon process involved. The NO(A 2Σ+) fragment, which was detected by ionization spectroscopy via the Rydberg ←A 2Σ+ transition, also required two-photon energy. These experimental data corroborate the existence of competing photodissociation product pathways, CH3 + NO2,CH3 + NO + O,CH3O + NO, and CH3NO + O, following the π → π* transition. The origins of the observed photofragments are discussed in this report along with recent theoretical studies and previous dynamics experiments performed at 193 nm.

Multiple product pathways in photodissociation of nitromethane at 213 nm.

PubMed

Sumida, Masataka; Kohge, Yasunori; Yamasaki, Katsuyoshi; Kohguchi, Hiroshi

2016-02-14

In this paper, we present a photodissociation dynamics study of nitromethane at 213 nm in the π → π(*) transition. Resonantly enhanced multiphoton ionization spectroscopy and ion-imaging were applied to measure the internal state distributions and state-resolved scattering distributions of the CH3, NO(X (2)Π, A (2)Σ(+)), and O((3)PJ) photofragments. The rotationally state-resolved scattering distribution of the CH3 fragment showed two velocity components, of which the slower one decreased the relative intensity as the rotational and vibrational excitations. The translational energy distribution of the faster CH3 fragment indicated the production of the NO2 counter-product in the electronic excited state, wherein 1 (2)B2 was the most probable. The NO(v = 0) fragment exhibited a bimodal translational energy distribution, whereas the NO(v = 1 and 2) fragment exhibited a single translational energy component with a relatively larger internal energy. The translational energy of a portion of the O((3)PJ) photofragment was found to be higher than the one-photon dissociation threshold, indicating the two-photon process involved. The NO(A (2)Σ(+)) fragment, which was detected by ionization spectroscopy via the Rydberg ← A (2)Σ(+) transition, also required two-photon energy. These experimental data corroborate the existence of competing photodissociation product pathways, CH3 + NO2,CH3 + NO + O,CH3O + NO, and CH3NO + O, following the π → π(*) transition. The origins of the observed photofragments are discussed in this report along with recent theoretical studies and previous dynamics experiments performed at 193 nm.

Failure probability under parameter uncertainty.

PubMed

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

A multistate dynamic site occupancy model for spatially aggregated sessile communities

USGS Publications Warehouse

Fukaya, Keiichi; Royle, J. Andrew; Okuda, Takehiro; Nakaoka, Masahiro; Noda, Takashi

2017-01-01

Estimation of transition probabilities of sessile communities seems easy in principle but may still be difficult in practice because resampling error (i.e. a failure to resample exactly the same location at fixed points) may cause significant estimation bias. Previous studies have developed novel analytical methods to correct for this estimation bias. However, they did not consider the local structure of community composition induced by the aggregated distribution of organisms that is typically observed in sessile assemblages and is very likely to affect observations.We developed a multistate dynamic site occupancy model to estimate transition probabilities that accounts for resampling errors associated with local community structure. The model applies a nonparametric multivariate kernel smoothing methodology to the latent occupancy component to estimate the local state composition near each observation point, which is assumed to determine the probability distribution of data conditional on the occurrence of resampling error.By using computer simulations, we confirmed that an observation process that depends on local community structure may bias inferences about transition probabilities. By applying the proposed model to a real data set of intertidal sessile communities, we also showed that estimates of transition probabilities and of the properties of community dynamics may differ considerably when spatial dependence is taken into account.Results suggest the importance of accounting for resampling error and local community structure for developing management plans that are based on Markovian models. Our approach provides a solution to this problem that is applicable to broad sessile communities. It can even accommodate an anisotropic spatial correlation of species composition, and may also serve as a basis for inferring complex nonlinear ecological dynamics.

Invasion resistance arises in strongly interacting species-rich model competition communities.

PubMed Central

Case, T J

1990-01-01

I assemble stable multispecies Lotka-Volterra competition communities that differ in resident species number and average strength (and variance) of species interactions. These are then invaded with randomly constructed invaders drawn from the same distribution as the residents. The invasion success rate and the fate of the residents are determined as a function of community-and species-level properties. I show that the probability of colonization success for an invader decreases with community size and the average strength of competition (alpha). Communities composed of many strongly interacting species limit the invasion possibilities of most similar species. These communities, even for a superior invading competitor, set up a sort of "activation barrier" that repels invaders when they invade at low numbers. This "priority effect" for residents is not assumed a priori in my description for the individual population dynamics of these species; rather it emerges because species-rich and strongly interacting species sets have alternative stable states that tend to disfavor species at low densities. These models point to community-level rather than invader-level properties as the strongest determinant of differences in invasion success. The probability of extinction for a resident species increases with community size, and the probability of successful colonization by the invader decreases. Thus an equilibrium community size results wherein the probability of a resident species' extinction just balances the probability of an invader's addition. Given the distribution of alpha it is now possible to predict the equilibrium species number. The results provide a logical framework for an island-biogeographic theory in which species turnover is low even in the face of persistent invasions and for the protection of fragile native species from invading exotics. PMID:11607132

Informing Disease Models with Temporal and Spatial Contact Structure among GPS-Collared Individuals in Wild Populations

PubMed Central

Williams, David M.; Dechen Quinn, Amy C.; Porter, William F.

2014-01-01

Contacts between hosts are essential for transmission of many infectious agents. Understanding how contacts, and thus transmission rates, occur in space and time is critical to effectively responding to disease outbreaks in free-ranging animal populations. Contacts between animals in the wild are often difficult to observe or measure directly. Instead, one must infer contacts from metrics such as proximity in space and time. Our objective was to examine how contacts between white-tailed deer (Odocoileus virginianus) vary in space and among seasons. We used GPS movement data from 71 deer in central New York State to quantify potential direct contacts between deer and indirect overlap in space use across time and space. Daily probabilities of direct contact decreased from winter (0.05–0.14), to low levels post-parturition through summer (0.00–0.02), and increased during the rut to winter levels. The cumulative distribution for the spatial structure of direct and indirect contact probabilities around a hypothetical point of occurrence increased rapidly with distance for deer pairs separated by 1,000 m – 7,000 m. Ninety-five percent of the probabilities of direct contact occurred among deer pairs within 8,500 m of one another, and 99% within 10,900 m. Probabilities of indirect contact accumulated across greater spatial extents: 95% at 11,900 m and 99% at 49,000 m. Contacts were spatially consistent across seasons, indicating that although contact rates differ seasonally, they occur proportionally across similar landscape extents. Distributions of contact probabilities across space can inform management decisions for assessing risk and allocating resources in response. PMID:24409293

A transformed path integral approach for solution of the Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Subramaniam, Gnana M.; Vedula, Prakash

2017-10-01

A novel path integral (PI) based method for solution of the Fokker-Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

Modeling stochastic noise in gene regulatory systems

PubMed Central

Meister, Arwen; Du, Chao; Li, Ye Henry; Wong, Wing Hung

2014-01-01

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems. PMID:25632368

Resonant Auger decay studies in Kr 3d{sub 3/2,5/2}{sup {minus}1}np states using angle-resolved electron imaging spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farhat, A.; Wills, A.A.; Berrah, N.

1999-01-01

An extensive and detailed mapping of the resonant Auger decay of all the photoexcited 3d{sub 3/2,5/2}{sup {minus}1}np states in Kr has been performed using angle-resolved two-dimensional photoelectron spectroscopy at the Advanced Light Source at Lawrence Berkeley National Laboratory. This has allowed us to obtain angular distributions and spectator and shake probabilities for the Kr 3d{sup {minus}1}np{r_arrow}4s{sup {minus}1}4p{sup {minus}1}({sup 1}P)mp+e{sup {minus}} (n=5{endash}9, m=5{endash}11) resonance Auger decays. The results show that the spectator-core coupling is strong at lower {ital n} (n=5,6) but lessens for higher {ital n}, with a shake-up of m=n+1 preferred. The observed trend is in good agreement with themore » previous experimental and theoretical spectator and shake probabilities for these transitions and also with the analogous decay to the 4s{sup 2}4p{sup 4}mp states [H. Aksela {ital et al.}, Phys. Rev. Lett. {bold 25}, 4970 (1997)]. However, to our knowledge, no prior angular distribution measurements for the Kr 3d{sup {minus}1}np{r_arrow}4s{sup {minus}1}4p{sup {minus}1}({sup 1}P)mp+e{sup {minus}} (n=5{endash}9, m=5{endash}11) resonant Auger decay has been reported. These are found to also show similar behavior to the decay to the 4s{sup 2}4p{sup 4}mp states. {copyright} {ital 1999} {ital The American Physical Society}« less

[Modeling of the financial reserves required by the livestock disease compensation fund of Lower Saxony for rebates in the course of disease outbreaks incorporating spatial restriction zones].

PubMed

Denzin, Nicolai; Gerdes, Ursula

2015-01-01

One of the tasks of the livestock disease compensation funds of the federal states in Germany is the financial compensation of livestock holders for livestock losses and costs incurred for disease control measures due to certain diseases. Usually, one half of these services are financed through financial reserves built up with the contributions paid by the owners of the respective animal species. The other half is covered by the federal state itself. But there is hardly any reference to how to calculate aforementioned financial reserves. Basically, following an approach presented recently regarding estimations concerning the compensation fund of the federal state of Saxony-Anhalt, in a stochastic modeling of the required reserves concerning the fund of Lower Saxony the anticipated costs within the spatial restriction zones allocated to outbreaks were incorporated for the first time. The overall costs (including the federal state's stakes), the share of the comnensation fund (required reserves) and the the partial costs for a total of 25 categories and subcategories and subcategories of livestock species making up the latter were estimated. It became evident that overall costs/the share of the fund were particularly determined among the diseases by foot-and-mouth disease and among the cost factors by the costs incurred for the compensation of livestock value within the areas surrounding the outbreaks in which all susceptible animals are killed (culling zone). The 80th, 90 and 95th percentile of the established probability distribution of the overall costs referred to a financial volume of about 312, 409 and 540 million euro, while the respective percentiles of the probability distribution of the required reserves of the compensation fund amounted to 175, 225 and 296 million euro.

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

NASA Technical Reports Server (NTRS)

Sankararaman, Shankar; Goebel, Kai

2013-01-01

This paper investigates the use of the inverse first-order reliability method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example.

The influence of persuasion in opinion formation and polarization

NASA Astrophysics Data System (ADS)

La Rocca, C. E.; Braunstein, L. A.; Vazquez, F.

2014-05-01

We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k=-M to totally in favor k = M. Same-orientation agents persuade each other with probability p, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q. The population initially evolves to (a) a polarized state for r=p/q\\gt 1 , where opinions' distribution is peaked at the extreme values k=+/- M , or (b) a centralized state for r < 1, with most opinions around k=+/- 1 . When r \\gg 1 , polarization lasts for a time that diverges as r^M \\ln N , where N is the population's size. Finally, an extremist consensus (k = M or -M ) is reached in a time that scales as r^{-1} for r \\ll 1 .

The Dynamics of Conditioning and Extinction

PubMed Central

Killeen, Peter R.; Sanabria, Federico; Dolgov, Igor

2009-01-01

Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts of responding to the CS. Responding depended on whether the prior trial contained a peck, food, or both. A linear-persistence/learning model moved animals into and out of a response state, and a Weibull distribution for number of within-trial responses governed in-state pecking. Variations of trial and inter-trial durations caused correlated changes in rate and probability of responding, and model parameters. A novel prediction—in the protracted absence of food, response rates can plateau above zero—was validated. The model predicted smooth acquisition functions when instantiated with the probability of food, but a more accurate jagged learning curve when instantiated with trial-to-trial records of reinforcement. The Skinnerian parameter was dominant only when food could be accelerated or delayed by pecking. These experiments provide a framework for trial-by-trial accounts of conditioning and extinction that increases the information available from the data, permitting them to comment more definitively on complex contemporary models of momentum and conditioning. PMID:19839699

A physically-based earthquake recurrence model for estimation of long-term earthquake probabilities

USGS Publications Warehouse

Ellsworth, William L.; Matthews, Mark V.; Nadeau, Robert M.; Nishenko, Stuart P.; Reasenberg, Paul A.; Simpson, Robert W.

1999-01-01

A physically-motivated model for earthquake recurrence based on the Brownian relaxation oscillator is introduced. The renewal process defining this point process model can be described by the steady rise of a state variable from the ground state to failure threshold as modulated by Brownian motion. Failure times in this model follow the Brownian passage time (BPT) distribution, which is specified by the mean time to failure, μ, and the aperiodicity of the mean, α (equivalent to the familiar coefficient of variation). Analysis of 37 series of recurrent earthquakes, M -0.7 to 9.2, suggests a provisional generic value of α = 0.5. For this value of α, the hazard function (instantaneous failure rate of survivors) exceeds the mean rate for times > μ⁄2, and is ~ ~ 2 ⁄ μ for all times > μ. Application of this model to the next M 6 earthquake on the San Andreas fault at Parkfield, California suggests that the annual probability of the earthquake is between 1:10 and 1:13.

Maceral distributions in Illinois coals and their paleoenvironmental implications

USGS Publications Warehouse

Harvey, R.D.; Dillon, J.W.

1985-01-01

For purposes of assessing the maceral distribution of Illinois (U.S.A.) coals analyses were assembled for 326 face channel and drill core samples from 24 coal members of the Pennsylvanian System. The inertinite content of coals from the Missourian and Virgilian Series averages 16.1% (mineral free), compared to 9.4% for older coals from the Desmoinesian and older Series. This indicates there was generally a higher state of oxidation in the peat that formed the younger coals. This state probably resulted from greater exposure of these peats to weathering as the climate became drier and the water table lower than was the case for the older coals, although oxidation during allochthonous deposition of inertinite components is a genetic factor that needs further study to confirm the importance of the climate. Regional variation of the vitrinite-inertinite ratio (V-I), on a mineral- and micrinite-free basis, was observed in the Springfield (No. 5) and Herrin (No. 6) Coal Members to be related to the geographical position of paleochannel (river) deposits known to have been contemporaneous with the peats that formed these two coal strata. The V-I ratio is highest (generally 12-27) in samples from areas adjacent to the channels, and lower (5-11) some 10-20 km away. We interpret the V-I ratio to be an inverse index of the degree of oxidation to which the original peat was exposed. High V-I ratio coal located near the channels probably formed under more anoxic conditions than did the lower V-I ratio coal some distance away from the channels. The low V-I ratio coal probably formed in areas of the peat swamp where the watertable was generally lower than the channel areas. ?? 1986.

The estimation of tree posterior probabilities using conditional clade probability distributions.

PubMed

Larget, Bret

2013-07-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample.

Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

NASA Astrophysics Data System (ADS)

Zuo, Weiguang; Liu, Ming; Fan, Tianhui; Wang, Pengtao

2018-06-01

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.

On the inequivalence of the CH and CHSH inequalities due to finite statistics

NASA Astrophysics Data System (ADS)

Renou, M. O.; Rosset, D.; Martin, A.; Gisin, N.

2017-06-01

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

Confidence as Bayesian Probability: From Neural Origins to Behavior.

PubMed

Meyniel, Florent; Sigman, Mariano; Mainen, Zachary F

2015-10-07

Research on confidence spreads across several sub-fields of psychology and neuroscience. Here, we explore how a definition of confidence as Bayesian probability can unify these viewpoints. This computational view entails that there are distinct forms in which confidence is represented and used in the brain, including distributional confidence, pertaining to neural representations of probability distributions, and summary confidence, pertaining to scalar summaries of those distributions. Summary confidence is, normatively, derived or "read out" from distributional confidence. Neural implementations of readout will trade off optimality versus flexibility of routing across brain systems, allowing confidence to serve diverse cognitive functions. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Saakian, David B.; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Exact probability distribution functions for Parrondo's games.

PubMed

Zadourian, Rubina; Saakian, David B; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Probability Distribution of Dose and Dose-Rate Effectiveness Factor for use in Estimating Risks of Solid Cancers From Exposure to Low-Let Radiation.

PubMed

Kocher, David C; Apostoaei, A Iulian; Hoffman, F Owen; Trabalka, John R

2018-06-01

This paper presents an analysis to develop a subjective state-of-knowledge probability distribution of a dose and dose-rate effectiveness factor for use in estimating risks of solid cancers from exposure to low linear energy transfer radiation (photons or electrons) whenever linear dose responses from acute and chronic exposure are assumed. A dose and dose-rate effectiveness factor represents an assumption that the risk of a solid cancer per Gy at low acute doses or low dose rates of low linear energy transfer radiation, RL, differs from the risk per Gy at higher acute doses, RH; RL is estimated as RH divided by a dose and dose-rate effectiveness factor, where RH is estimated from analyses of dose responses in Japanese atomic-bomb survivors. A probability distribution to represent uncertainty in a dose and dose-rate effectiveness factor for solid cancers was developed from analyses of epidemiologic data on risks of incidence or mortality from all solid cancers as a group or all cancers excluding leukemias, including (1) analyses of possible nonlinearities in dose responses in atomic-bomb survivors, which give estimates of a low-dose effectiveness factor, and (2) comparisons of risks in radiation workers or members of the public from chronic exposure to low linear energy transfer radiation at low dose rates with risks in atomic-bomb survivors, which give estimates of a dose-rate effectiveness factor. Probability distributions of uncertain low-dose effectiveness factors and dose-rate effectiveness factors for solid cancer incidence and mortality were combined using assumptions about the relative weight that should be assigned to each estimate to represent its relevance to estimation of a dose and dose-rate effectiveness factor. The probability distribution of a dose and dose-rate effectiveness factor for solid cancers developed in this study has a median (50th percentile) and 90% subjective confidence interval of 1.3 (0.47, 3.6). The harmonic mean is 1.1, which implies that the arithmetic mean of an uncertain estimate of the risk of a solid cancer per Gy at low acute doses or low dose rates of low linear energy transfer radiation is only about 10% less than the mean risk per Gy at higher acute doses. Data were also evaluated to define a low acute dose or low dose rate of low linear energy transfer radiation, i.e., a dose or dose rate below which a dose and dose-rate effectiveness factor should be applied in estimating risks of solid cancers.

Rickettsia parkeri rickettsiosis and its clinical distinction from Rocky Mountain spotted fever.

PubMed

Paddock, Christopher D; Finley, Richard W; Wright, Cynthia S; Robinson, Howard N; Schrodt, Barbara J; Lane, Carole C; Ekenna, Okechukwu; Blass, Mitchell A; Tamminga, Cynthia L; Ohl, Christopher A; McLellan, Susan L F; Goddard, Jerome; Holman, Robert C; Openshaw, John J; Sumner, John W; Zaki, Sherif R; Eremeeva, Marina E

2008-11-01

Rickettsia parkeri rickettsiosis, a recently identified spotted fever transmitted by the Gulf Coast tick (Amblyomma maculatum), was first described in 2004. We summarize the clinical and epidemiological features of 12 patients in the United States with confirmed or probable disease attributable to R. parkeri and comment on distinctions between R. parkeri rickettsiosis and other United States rickettsioses. Clinical specimens from patients in the United States who reside within the range of A. maculatum for whom an eschar or vesicular rash was described were evaluated by > or =1 laboratory assays at the Centers for Disease Control and Prevention (Atlanta, GA) to identify probable or confirmed infection with R. parkeri. During 1998-2007, clinical samples from 12 patients with illnesses epidemiologically and clinically compatible with R. parkeri rickettsiosis were submitted for diagnostic evaluation. Using indirect immunofluorescence antibody assays, immunohistochemistry, polymerase chain reaction assays, and cell culture isolation, we identified 6 confirmed and 6 probable cases of infection with R. parkeri. The aggregate clinical characteristics of these patients revealed a disease similar to but less severe than classically described Rocky Mountain spotted fever. Closer attention to the distinct clinical features of the various spotted fever syndromes that exist in the United States and other countries of the Western hemisphere, coupled with more frequent use of specific confirmatory assays, may unveil several unique diseases that have been identified collectively as Rocky Mountain spotted fever during the past century. Accurate assessments of these distinct infections will ultimately provide a more valid description of the currently recognized distribution, incidence, and case-fatality rate of Rocky Mountain spotted fever.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

Constructions of secure entanglement channels assisted by quantum dots inside single-sided optical cavities

NASA Astrophysics Data System (ADS)

Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Choi, Seong-Gon; Hong, Jong-Phil

2017-08-01

We propose quantum information processing schemes to generate and swap entangled states based on the interactions between flying photons and quantum dots (QDs) confined within optical cavities for quantum communication. To produce and distribute entangled states (Bell and Greenberger-Horne-Zeilinger [GHZ] states) between the photonic qubits of flying photons of consumers (Alice and Bob) and electron-spin qubits of a provider (trust center, or TC), the TC employs the interactions of the QD-cavity system, which is composed of a charged QD (negatively charged exciton) inside a single-sided cavity. Subsequently, the TC constructs an entanglement channel (Bell state and 4-qubit GHZ state) to link one consumer with another through entanglement swapping, which can be realized to exploit a probe photon with interactions of the QD-cavity systems and single-qubit measurements without Bell state measurement, for quantum communication between consumers. Consequently, the TC, which has quantum nodes (QD-cavity systems), can accomplish constructing the entanglement channel (authenticated channel) between two separated consumers from the distributions of entangled states and entanglement swapping. Furthermore, our schemes using QD-cavity systems, which are feasible with a certain probability of success and high fidelity, can be experimentally implemented with technology currently in use.

Information flow in an atmospheric model and data assimilation

NASA Astrophysics Data System (ADS)

Yoon, Young-noh

2011-12-01

Weather forecasting consists of two processes, model integration and analysis (data assimilation). During the model integration, the state estimate produced by the analysis evolves to the next cycle time according to the atmospheric model to become the background estimate. The analysis then produces a new state estimate by combining the background state estimate with new observations, and the cycle repeats. In an ensemble Kalman filter, the probability distribution of the state estimate is represented by an ensemble of sample states, and the covariance matrix is calculated using the ensemble of sample states. We perform numerical experiments on toy atmospheric models introduced by Lorenz in 2005 to study the information flow in an atmospheric model in conjunction with ensemble Kalman filtering for data assimilation. This dissertation consists of two parts. The first part of this dissertation is about the propagation of information and the use of localization in ensemble Kalman filtering. If we can perform data assimilation locally by considering the observations and the state variables only near each grid point, then we can reduce the number of ensemble members necessary to cover the probability distribution of the state estimate, reducing the computational cost for the data assimilation and the model integration. Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. We address these issues and elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. The second part of this dissertation is about ensemble regional data assimilation using joint states. Assuming that we have a global model and a regional model of higher accuracy defined in a subregion inside the global region, we propose a data assimilation scheme that produces the analyses for the global and the regional model simultaneously, considering forecast information from both models. We show that our new data assimilation scheme produces better results both in the subregion and the global region than the data assimilation scheme that produces the analyses for the global and the regional model separately.

Seasonal climate variation and caribou availability: Modeling sequential movement using satellite-relocation data

USGS Publications Warehouse

Nicolson, Craig; Berman, Matthew; West, Colin Thor; Kofinas, Gary P.; Griffith, Brad; Russell, Don; Dugan, Darcy

2013-01-01

Livelihood systems that depend on mobile resources must constantly adapt to change. For people living in permanent settlements, environmental changes that affect the distribution of a migratory species may reduce the availability of a primary food source, with the potential to destabilize the regional social-ecological system. Food security for Arctic indigenous peoples harvesting barren ground caribou (Rangifer tarandus granti) depends on movement patterns of migratory herds. Quantitative assessments of physical, ecological, and social effects on caribou distribution have proven difficult because of the significant interannual variability in seasonal caribou movement patterns. We developed and evaluated a modeling approach for simulating the distribution of a migratory herd throughout its annual cycle over a multiyear period. Beginning with spatial and temporal scales developed in previous studies of the Porcupine Caribou Herd of Canada and Alaska, we used satellite collar locations to compute and analyze season-by-season probabilities of movement of animals between habitat zones under two alternative weather conditions for each season. We then built a set of transition matrices from these movement probabilities, and simulated the sequence of movements across the landscape as a Markov process driven by externally imposed seasonal weather states. Statistical tests showed that the predicted distributions of caribou were consistent with observed distributions, and significantly correlated with subsistence harvest levels for three user communities. Our approach could be applied to other caribou herds and could be adapted for simulating the distribution of other ungulates and species with similarly large interannual variability in the use of their range.